%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG249^3 : 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 : 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 08:05:38 AM UTC 2026 % Result : Theorem 0.39s 0.73s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG249^3 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n005.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 01:54:33 EDT 2026 % 0.16/0.34 % CPUTime : % 0.38/0.56 %----Proving TH0 % 0.39/0.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.73 % SZS status Theorem % 0.39/0.73 % SZS output start Proof % 0.39/0.73 ( % 0.39/0.73 (declare-sort tptp.term 0) % 0.39/0.73 (declare-sort tptp.subst 0) % 0.39/0.73 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.39/0.73 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.39/0.73 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.39/0.73 (declare-const tptp.one tptp.term) % 0.39/0.73 (declare-const tptp.sh tptp.subst) % 0.39/0.73 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.39/0.73 (declare-const tptp.var (-> tptp.term Bool)) % 0.39/0.73 (declare-const tptp.id tptp.subst) % 0.39/0.73 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3b Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3a Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3 Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem2 Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem1 Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasinduction_lem0 Bool) % 0.39/0.73 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasapnotvar Bool) % 0.39/0.73 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.39/0.73 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.39/0.73 (declare-const tptp.hoaslamnotvar Bool) % 0.39/0.73 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.39/0.73 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.39/0.73 (declare-const tptp.hoaslamnotap Bool) % 0.39/0.73 (declare-const tptp.hoaslaminj_lthm Bool) % 0.39/0.73 (declare-const tptp.hoaslaminj_gthm Bool) % 0.39/0.73 (declare-const tptp.hoaslaminj Bool) % 0.39/0.73 (declare-const tptp.hoasapinj2_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasapinj2_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasapinj2 Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.39/0.73 (declare-const tptp.axassoc Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.39/0.73 (declare-const tptp.axvarcons Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem0 Bool) % 0.39/0.73 (declare-const tptp.apinj1 Bool) % 0.39/0.73 (declare-const tptp.induction Bool) % 0.39/0.73 (declare-const tptp.apnotvar Bool) % 0.39/0.73 (declare-const tptp.laminj Bool) % 0.39/0.73 (declare-const tptp.axvarshift Bool) % 0.39/0.73 (declare-const tptp.ulamvarind Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.39/0.73 (declare-const tptp.ulamvarsh Bool) % 0.39/0.73 (declare-const tptp.ulamvar1 Bool) % 0.39/0.73 (declare-const tptp.axabs Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem1 Bool) % 0.39/0.73 (declare-const tptp.shinj Bool) % 0.39/0.73 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.39/0.73 (declare-const tptp.apinj2 Bool) % 0.39/0.73 (declare-const tptp.axvarid Bool) % 0.39/0.73 (declare-const tptp.axidl Bool) % 0.39/0.73 (declare-const tptp.axclos Bool) % 0.39/0.73 (declare-const tptp.termmset Bool) % 0.39/0.73 (declare-const tptp.axshiftcons Bool) % 0.39/0.73 (declare-const tptp.lamnotap Bool) % 0.39/0.73 (declare-const tptp.lamnotvar Bool) % 0.39/0.73 (declare-const tptp.axapp Bool) % 0.39/0.73 (declare-const tptp.axscons Bool) % 0.39/0.73 (declare-const tptp.axmap Bool) % 0.39/0.73 (declare-const tptp.axidr Bool) % 0.39/0.73 (declare-const tptp.induction2lem Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasapinj1_lthm Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem1v2 Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.39/0.73 (declare-const tptp.induction2 Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem2v2 Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem3v2 Bool) % 0.39/0.73 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.39/0.73 (declare-const tptp.pushprop Bool) % 0.39/0.73 (declare-const tptp.pushprop_gthm Bool) % 0.39/0.73 (declare-const tptp.hoasapinj1 Bool) % 0.39/0.73 (declare-const tptp.pushprop_lthm_orig Bool) % 0.39/0.73 (declare-const tptp.pushprop_lthm Bool) % 0.39/0.73 (declare-const tptp.induction2lem_gthm Bool) % 0.39/0.73 (declare-const tptp.induction2lem_lthm Bool) % 0.39/0.73 (declare-const tptp.induction2_gthm Bool) % 0.39/0.73 (declare-const tptp.induction2_lthm Bool) % 0.39/0.73 (declare-const tptp.substmonoid Bool) % 0.39/0.73 (declare-const tptp.substmonoid_gthm Bool) % 0.39/0.73 (declare-const tptp.termmset_gthm Bool) % 0.39/0.73 (declare-const tptp.substmonoid_lthm Bool) % 0.39/0.73 (declare-const tptp.termmset_lthm Bool) % 0.39/0.73 (declare-const tptp.hoasapinj1_gthm Bool) % 0.39/0.73 (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)))))))))))) % 0.39/0.73 (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)))))) % 0.39/0.73 (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))))) % 0.39/0.73 (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)))))) % 0.39/0.73 (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)))))))) % 0.39/0.73 (define @t1 () (@var "M" tptp.subst)) % 0.39/0.73 (define @t2 () (@var "B" tptp.term)) % 0.39/0.73 (define @t3 () (_ tptp.sub @t2)) % 0.39/0.73 (define @t4 () (_ @t3 @t1)) % 0.39/0.73 (define @t5 () (@var "A" tptp.term)) % 0.39/0.73 (define @t6 () (_ tptp.sub @t5)) % 0.39/0.73 (define @t7 () (_ @t6 @t1)) % 0.39/0.73 (define @t8 () (_ tptp.ap @t5)) % 0.39/0.73 (define @t9 () (_ @t8 @t2)) % 0.39/0.73 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.39/0.73 (define @t11 () (_ tptp.sub tptp.one)) % 0.39/0.73 (define @t12 () (@list @t5 @t1)) % 0.39/0.73 (define @t13 () (@list @t5)) % 0.39/0.73 (define @t14 () (forall @t13 (= (_ @t6 tptp.id) @t5))) % 0.39/0.73 (define @t15 () (_ tptp.comp @t1)) % 0.39/0.73 (define @t16 () (_ tptp.push tptp.one)) % 0.39/0.73 (define @t17 () (_ tptp.lam @t5)) % 0.39/0.73 (define @t18 () (@var "N" tptp.subst)) % 0.39/0.73 (define @t19 () (_ @t15 @t18)) % 0.39/0.73 (define @t20 () (_ @t6 @t19)) % 0.39/0.73 (define @t21 () (_ (_ tptp.sub @t7) @t18)) % 0.39/0.73 (define @t22 () (= @t21 @t20)) % 0.39/0.73 (define @t23 () (@list @t5 @t1 @t18)) % 0.39/0.73 (define @t24 () (forall @t23 @t22)) % 0.39/0.73 (define @t25 () (= tptp.axclos @t24)) % 0.39/0.73 (define @t26 () (@list @t1)) % 0.39/0.73 (define @t27 () (forall @t26 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 0.39/0.73 (define @t28 () (_ tptp.comp tptp.sh)) % 0.39/0.73 (define @t29 () (_ @t28 @t10)) % 0.39/0.73 (define @t30 () (forall @t12 (= @t29 @t1))) % 0.39/0.73 (define @t31 () (= tptp.axshiftcons @t30)) % 0.39/0.73 (define @t32 () (@var "K" tptp.subst)) % 0.39/0.73 (define @t33 () (forall (@list @t1 @t18 @t32) (= (_ (_ tptp.comp @t19) @t32) (_ @t15 (_ (_ tptp.comp @t18) @t32))))) % 0.39/0.73 (define @t34 () (_ @t6 @t18)) % 0.39/0.73 (define @t35 () (_ (_ tptp.push @t34) @t19)) % 0.39/0.73 (define @t36 () (forall @t26 (= (_ @t15 tptp.id) @t1))) % 0.39/0.73 (define @t37 () (_ @t16 tptp.sh)) % 0.39/0.73 (define @t38 () (_ @t6 tptp.sh)) % 0.39/0.73 (define @t39 () (_ tptp.var @t5)) % 0.39/0.73 (define @t40 () (@var "P" (-> tptp.term Bool))) % 0.39/0.73 (define @t41 () (_ @t40 @t5)) % 0.39/0.73 (define @t42 () (forall @t13 (=> @t39 @t41))) % 0.39/0.73 (define @t43 () (@list @t40)) % 0.39/0.73 (define @t44 () (= @t5 @t2)) % 0.39/0.73 (define @t45 () (@var "D" tptp.term)) % 0.39/0.73 (define @t46 () (_ tptp.ap @t2)) % 0.39/0.73 (define @t47 () (@var "C" tptp.term)) % 0.39/0.73 (define @t48 () (= (_ @t8 @t47) (_ @t46 @t45))) % 0.39/0.73 (define @t49 () (@list @t5 @t2 @t47 @t45)) % 0.39/0.73 (define @t50 () (= @t47 @t45)) % 0.39/0.73 (define @t51 () (@list @t5 @t2)) % 0.39/0.73 (define @t52 () (forall @t13 @t41)) % 0.39/0.73 (define @t53 () (_ @t40 @t17)) % 0.39/0.73 (define @t54 () (_ @t40 @t2)) % 0.39/0.73 (define @t55 () (forall @t51 (=> @t41 (=> @t54 (_ @t40 @t9))))) % 0.39/0.73 (define @t56 () (@var "Q" (-> tptp.term Bool))) % 0.39/0.73 (define @t57 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t40) @t56)) % 0.39/0.73 (define @t58 () (@list @t56)) % 0.39/0.73 (define @t59 () (@list @t40 @t5 @t1)) % 0.39/0.73 (define @t60 () (_ tptp.push @t2)) % 0.39/0.73 (define @t61 () (@var "K" (-> tptp.term Bool))) % 0.39/0.73 (define @t62 () (@list @t40 @t56 @t5 @t1)) % 0.39/0.73 (define @t63 () (_ tptp.sub @t47)) % 0.39/0.73 (define @t64 () (_ @t63 tptp.sh)) % 0.39/0.73 (define @t65 () (_ @t56 @t64)) % 0.39/0.73 (define @t66 () (_ @t56 @t47)) % 0.39/0.73 (define @t67 () (=> @t66 @t65)) % 0.39/0.73 (define @t68 () (_ tptp.var @t47)) % 0.39/0.73 (define @t69 () (@list @t47)) % 0.39/0.73 (define @t70 () (forall @t69 (=> @t68 @t67))) % 0.39/0.73 (define @t71 () (_ @t40 @t4)) % 0.39/0.73 (define @t72 () (_ tptp.var @t2)) % 0.39/0.73 (define @t73 () (@list @t2)) % 0.39/0.73 (define @t74 () (forall @t73 (=> @t72 @t71))) % 0.39/0.73 (define @t75 () (=> @t74 @t70)) % 0.39/0.73 (define @t76 () (=> @t57 @t75)) % 0.39/0.73 (define @t77 () (forall @t62 @t76)) % 0.39/0.73 (define @t78 () (= tptp.pushprop_lem2v2 @t77)) % 0.39/0.73 (define @t79 () (=> tptp.axshiftcons tptp.pushprop_lem2v2)) % 0.39/0.73 (define @t80 () (=> tptp.axclos @t79)) % 0.39/0.73 (define @t81 () (= tptp.pushprop_lem2v2_lthm @t80)) % 0.39/0.73 (define @t82 () (_ @t3 @t10)) % 0.39/0.73 (define @t83 () (forall @t73 (=> @t72 (_ @t40 @t82)))) % 0.39/0.73 (define @t84 () (_ @t56 @t2)) % 0.39/0.73 (define @t85 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.39/0.73 (define @t86 () (_ @t6 (_ @t60 tptp.id))) % 0.39/0.73 (define @t87 () (forall @t13 (=> (forall @t73 (=> @t54 (_ @t40 @t86))) @t53))) % 0.39/0.73 (define @t88 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.39/0.73 (define @t89 () (=> tptp.induction2lem tptp.induction2)) % 0.39/0.73 (define @t90 () (_ tptp.hoasap tptp.id)) % 0.39/0.73 (define @t91 () (_ (_ @t90 @t5) tptp.id)) % 0.39/0.73 (define @t92 () (= (_ @t91 @t47) (_ (_ (_ @t90 @t2) tptp.id) @t45))) % 0.39/0.73 (define @t93 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.73 (define @t94 () (_ (_ @t93 @t1) @t5)) % 0.39/0.73 (define @t95 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.73 (define @t96 () (_ @t95 @t1)) % 0.39/0.73 (define @t97 () (_ @t96 @t5)) % 0.39/0.73 (define @t98 () (@list @t1 @t5)) % 0.39/0.73 (define @t99 () (_ tptp.hoaslam tptp.id)) % 0.39/0.73 (define @t100 () (_ @t99 (lambda @t98 @t97))) % 0.39/0.73 (define @t101 () (@list @t1 @t5 @t18)) % 0.39/0.73 (define @t102 () (_ (_ @t95 @t19) @t34)) % 0.39/0.73 (define @t103 () (_ (_ tptp.sub @t97) @t18)) % 0.39/0.73 (define @t104 () (forall @t101 (= @t103 @t102))) % 0.39/0.73 (define @t105 () (@list @t95)) % 0.39/0.73 (define @t106 () (_ @t91 @t2)) % 0.39/0.73 (define @t107 () (_ tptp.hoasvar tptp.id)) % 0.39/0.73 (define @t108 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.39/0.73 (define @t109 () (_ (_ tptp.hoasinduction_p_and_p_prime @t108) @t56)) % 0.39/0.73 (define @t110 () (@list @t108)) % 0.39/0.73 (define @t111 () (_ @t56 @t5)) % 0.39/0.73 (define @t112 () (_ @t108 tptp.id)) % 0.39/0.73 (define @t113 () (_ (_ @t112 @t5) tptp.id)) % 0.39/0.73 (define @t114 () (forall @t13 (=> (_ (_ @t107 @t5) tptp.id) @t113))) % 0.39/0.73 (define @t115 () (_ (_ (_ @t108 @t1) @t5) (_ (_ tptp.comp @t32) @t18))) % 0.39/0.73 (define @t116 () (_ (_ (_ @t108 (_ @t15 @t32)) (_ @t6 @t32)) @t18)) % 0.39/0.73 (define @t117 () (@list @t1 @t5 @t18 @t32)) % 0.39/0.73 (define @t118 () (forall @t117 (=> @t116 @t115))) % 0.39/0.73 (define @t119 () (forall @t117 (=> @t115 @t116))) % 0.39/0.73 (define @t120 () (@list @t108 @t56)) % 0.39/0.73 (define @t121 () (_ (_ @t112 @t2) tptp.id)) % 0.39/0.73 (define @t122 () (forall @t51 (=> @t113 (=> @t121 (_ (_ @t112 @t106) tptp.id))))) % 0.39/0.73 (define @t123 () (=> (forall @t13 (=> @t113 (_ (_ @t112 (_ (_ @t95 tptp.id) @t5)) tptp.id))) (_ (_ @t112 @t100) tptp.id))) % 0.39/0.73 (define @t124 () (forall @t105 (=> @t104 @t123))) % 0.39/0.73 (define @t125 () (=> @t124 (=> @t109 (forall @t13 (=> (forall @t73 (=> @t84 (_ @t56 @t86))) (_ @t56 @t17)))))) % 0.39/0.73 (define @t126 () (=> 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))))))))))))))))))))))))))))))))))) % 0.39/0.73 (define @t127 () (=> 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))))))))))))))))))))))))))))))))))) % 0.39/0.73 (define @t128 () (forall @t73 (=> @t121 (_ (_ @t112 @t86) tptp.id)))) % 0.39/0.73 (define @t129 () (forall @t13 (=> @t128 (_ (_ @t112 (_ tptp.lam (_ @t6 @t37))) tptp.id)))) % 0.39/0.73 (define @t130 () (=> @t124 (forall @t13 (=> @t128 (_ (_ @t112 @t17) tptp.id))))) % 0.39/0.73 (define @t131 () (_ (_ @t95 tptp.sh) tptp.one)) % 0.39/0.73 (define @t132 () (=> @t122 (=> @t124 (forall @t13 @t113)))) % 0.39/0.73 (define @t133 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.39/0.73 (define @t134 () (not tptp.pushprop_lem2v2_lthm)) % 0.39/0.73 (define @t135 () (@var "X" tptp.term)) % 0.39/0.73 (define @t136 () (_ tptp.sub @t135)) % 0.39/0.73 (define @t137 () (_ @t136 @t10)) % 0.39/0.73 (define @t138 () (_ @t40 @t137)) % 0.39/0.73 (define @t139 () (_ @t56 @t135)) % 0.39/0.73 (define @t140 () (= @t139 @t138)) % 0.39/0.73 (define @t141 () (@list @t135)) % 0.39/0.73 (define @t142 () (forall @t141 @t140)) % 0.39/0.73 (define @t143 () (@list @t5 @t1 @t40 @t56)) % 0.39/0.73 (define @t144 () (lambda @t143 @t142)) % 0.39/0.73 (define @t145 () (lambda (@list @t1 @t5 @t18 @t2) (_ (_ tptp.ap @t34) @t2))) % 0.39/0.73 (define @t146 () (lambda (@list @t1 @t95) (_ tptp.lam @t131))) % 0.39/0.73 (define @t147 () (lambda @t101 (_ tptp.var @t34))) % 0.39/0.73 (define @t148 () (lambda @t120 (forall @t141 (= @t139 (_ (_ @t112 @t135) tptp.id))))) % 0.39/0.73 (define @t149 () (@var "BOUND_VARIABLE_9263" tptp.term)) % 0.39/0.73 (define @t150 () (_ @t56 (tptp.sub @t149 tptp.sh))) % 0.39/0.73 (define @t151 () (not (_ @t56 @t149))) % 0.39/0.73 (define @t152 () (not (tptp.var @t149))) % 0.39/0.73 (define @t153 () (tptp.sub @t2 @t1)) % 0.39/0.73 (define @t154 () (_ @t40 @t153)) % 0.39/0.73 (define @t155 () (tptp.var @t2)) % 0.39/0.73 (define @t156 () (not @t155)) % 0.39/0.73 (define @t157 () (forall @t73 (or @t156 @t154))) % 0.39/0.73 (define @t158 () (not @t157)) % 0.39/0.73 (define @t159 () (tptp.push @t5 @t1)) % 0.39/0.73 (define @t160 () (tptp.sub @t135 @t159)) % 0.39/0.73 (define @t161 () (_ @t40 @t160)) % 0.39/0.73 (define @t162 () (_ @t56 @t135)) % 0.39/0.73 (define @t163 () (forall @t141 (= @t162 @t161))) % 0.39/0.73 (define @t164 () (not @t163)) % 0.39/0.73 (define @t165 () (or @t164 @t158 @t152 @t151 @t150)) % 0.39/0.73 (define @t166 () (or @t152 @t151 @t150)) % 0.39/0.73 (define @t167 () (or @t164 @t158 @t166)) % 0.39/0.73 (define @t168 () (@list @t40 @t56 @t5 @t1 @t149)) % 0.39/0.73 (define @t169 () (forall @t168 @t167)) % 0.39/0.73 (define @t170 () (@list @t149)) % 0.39/0.73 (define @t171 () (forall @t170 @t167)) % 0.39/0.73 (define @t172 () (forall @t170 @t166)) % 0.39/0.73 (define @t173 () (or @t164 @t158 @t172)) % 0.39/0.73 (define @t174 () (tptp.sub @t47 tptp.sh)) % 0.39/0.73 (define @t175 () (_ @t56 @t174)) % 0.39/0.73 (define @t176 () (_ @t56 @t47)) % 0.39/0.73 (define @t177 () (tptp.var @t47)) % 0.39/0.73 (define @t178 () (forall @t69 (or (not @t177) (not @t176) @t175))) % 0.39/0.73 (define @t179 () (or @t164 @t158 @t178)) % 0.39/0.73 (define @t180 () (=> @t157 @t178)) % 0.39/0.73 (define @t181 () (not @t66)) % 0.39/0.73 (define @t182 () (not @t68)) % 0.39/0.73 (define @t183 () (or @t182 @t181 @t65)) % 0.39/0.73 (define @t184 () (not @t72)) % 0.39/0.73 (define @t185 () (or @t184 @t71)) % 0.39/0.73 (define @t186 () (lambda @t58 @t163)) % 0.39/0.73 (define @t187 () (lambda (@list @t40 @t56) @t163)) % 0.39/0.73 (define @t188 () (lambda (@list @t1 @t40 @t56) @t163)) % 0.39/0.73 (define @t189 () (_ (lambda @t143 @t163) @t5)) % 0.39/0.73 (define @t190 () (=> (_ (_ (_ @t189 @t1) @t40) @t56) @t75)) % 0.39/0.73 (define @t191 () (forall @t62 @t190)) % 0.39/0.73 (define @t192 () (tptp.comp tptp.sh @t159)) % 0.39/0.73 (define @t193 () (= @t1 @t29)) % 0.39/0.73 (define @t194 () (tptp.comp @t1 @t18)) % 0.39/0.73 (define @t195 () (tptp.sub @t5 @t194)) % 0.39/0.73 (define @t196 () (tptp.sub @t5 @t1)) % 0.39/0.73 (define @t197 () (tptp.sub @t196 @t18)) % 0.39/0.73 (define @t198 () (forall @t168 @t165)) % 0.39/0.73 (define @t199 () (@quantifiers_skolemize @t198 3)) % 0.39/0.73 (define @t200 () (@quantifiers_skolemize @t198 2)) % 0.39/0.73 (define @t201 () (tptp.push @t200 @t199)) % 0.39/0.73 (define @t202 () (@quantifiers_skolemize @t198 0)) % 0.39/0.73 (define @t203 () (@quantifiers_skolemize @t198 1)) % 0.39/0.73 (define @t204 () (forall @t141 (= (_ @t203 @t135) (_ @t202 (tptp.sub @t135 @t201))))) % 0.39/0.73 (define @t205 () (@quantifiers_skolemize @t198 4)) % 0.39/0.73 (define @t206 () (tptp.sub @t205 tptp.sh)) % 0.39/0.73 (define @t207 () (_ @t203 @t206)) % 0.39/0.73 (define @t208 () (tptp.var @t205)) % 0.39/0.73 (define @t209 () (not @t208)) % 0.39/0.73 (define @t210 () (forall @t73 (or @t156 (_ @t202 (tptp.sub @t2 @t199))))) % 0.39/0.73 (define @t211 () (not @t210)) % 0.39/0.73 (define @t212 () (not @t204)) % 0.39/0.73 (define @t213 () (or @t212 @t211 @t209 (not (_ @t203 @t205)) @t207)) % 0.39/0.73 (define @t214 () (@list true)) % 0.39/0.73 (define @t215 () (@list @t213)) % 0.39/0.73 (define @t216 () (_ @t202 (tptp.sub @t206 @t201))) % 0.39/0.73 (define @t217 () (= @t207 @t216)) % 0.39/0.73 (define @t218 () (not @t216)) % 0.39/0.73 (define @t219 () (tptp.sub @t205 @t199)) % 0.39/0.73 (define @t220 () (_ @t202 @t219)) % 0.39/0.73 (define @t221 () (or @t209 @t220)) % 0.39/0.73 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.39/0.73 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.39/0.73 (assume @p3 (= tptp.axvarid @t14)) % 0.39/0.73 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t17) @t1) (_ tptp.lam (_ @t6 (_ @t16 (_ @t15 tptp.sh)))))))) % 0.39/0.73 (assume @p5 @t25) % 0.39/0.73 (assume @p6 (= tptp.axidl @t27)) % 0.39/0.73 (assume @p7 @t31) % 0.39/0.73 (assume @p8 (= tptp.axassoc @t33)) % 0.39/0.73 (assume @p9 (= tptp.axmap (forall @t23 (= (_ (_ tptp.comp @t10) @t18) @t35)))) % 0.39/0.73 (assume @p10 (= tptp.axidr @t36)) % 0.39/0.73 (assume @p11 (= tptp.axvarshift (= @t37 tptp.id))) % 0.39/0.73 (assume @p12 (= tptp.axscons (forall @t26 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t28 @t1)) @t1)))) % 0.39/0.73 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.39/0.73 (assume @p14 (= tptp.ulamvarsh (forall @t13 (=> @t39 (_ tptp.var @t38))))) % 0.39/0.73 (assume @p15 (= tptp.ulamvarind (forall @t43 (=> (_ @t40 tptp.one) (=> (forall @t13 (=> @t39 (=> @t41 (_ @t40 @t38)))) @t42))))) % 0.39/0.73 (assume @p16 (= tptp.apinj1 (forall @t49 (=> @t48 @t44)))) % 0.39/0.73 (assume @p17 (= tptp.apinj2 (forall @t49 (=> @t48 @t50)))) % 0.39/0.73 (assume @p18 (= tptp.laminj (forall @t51 (=> (= @t17 (_ tptp.lam @t2)) @t44)))) % 0.39/0.73 (assume @p19 (= tptp.shinj (forall @t51 (=> (= @t38 (_ @t3 tptp.sh)) @t44)))) % 0.39/0.73 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t47) (not (= @t17 (_ @t46 @t47)))))) % 0.39/0.73 (assume @p21 (= tptp.apnotvar (forall @t51 (not (_ tptp.var @t9))))) % 0.39/0.73 (assume @p22 (= tptp.lamnotvar (forall @t13 (not (_ tptp.var @t17))))) % 0.39/0.73 (assume @p23 (= tptp.induction (forall @t43 (=> @t42 (=> @t55 (=> (forall @t13 (=> @t41 @t53)) @t52)))))) % 0.39/0.73 (assume @p24 (= tptp.pushprop_lem0 (forall @t59 (exists @t58 @t57)))) % 0.39/0.73 (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))))))))))))))))))))))))) % 0.39/0.73 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.39/0.73 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t40 @t61 @t5 @t1 @t2) (=> @t41 (_ @t61 (_ @t6 (_ @t60 @t1))))))) % 0.39/0.73 (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))))))))))))))))))))))))) % 0.39/0.73 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.39/0.73 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t62 (=> @t41 (=> @t57 (_ @t56 tptp.one)))))) % 0.39/0.73 (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))))))))))))))))))))))))) % 0.39/0.73 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.39/0.73 (assume @p33 @t78) % 0.39/0.73 (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))))))))))))))))))))))))) % 0.39/0.73 (assume @p35 @t81) % 0.39/0.73 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t62 (=> @t57 (=> (forall @t73 (=> @t72 @t84)) @t83))))) % 0.39/0.73 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.39/0.73 (assume @p38 (= tptp.pushprop (forall @t59 (=> @t74 (=> @t41 @t83))))) % 0.39/0.73 (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))))))))))))))))))))))))) % 0.39/0.73 (assume @p40 (= tptp.pushprop_lthm_orig @t85)) % 0.39/0.73 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t85))) % 0.39/0.73 (assume @p42 (= tptp.induction2lem (forall @t43 (=> @t55 (=> @t87 (forall @t12 (=> @t74 (_ @t40 @t7)))))))) % 0.39/0.73 (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 @t88)))))))))))))))))))))))) % 0.39/0.73 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t88)))))))))) % 0.39/0.73 (assume @p45 (= tptp.induction2 (forall @t43 (=> @t42 (=> @t55 (=> @t87 @t52)))))) % 0.39/0.73 (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 @t89)))))))))))))))))))))))))) % 0.39/0.73 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t89))) % 0.39/0.73 (assume @p48 (= tptp.substmonoid (and @t33 @t27 @t36))) % 0.39/0.73 (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)))))))))))))))))))))))))))) % 0.39/0.73 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.39/0.73 (assume @p51 (= tptp.termmset (and @t24 @t14))) % 0.39/0.73 (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))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.39/0.73 (assume @p54 (= tptp.hoasapinj1 (forall @t49 (=> @t92 @t44)))) % 0.39/0.73 (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)))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.39/0.73 (assume @p57 (= tptp.hoasapinj2 (forall @t49 (=> @t92 @t50)))) % 0.39/0.73 (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))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.39/0.73 (assume @p60 (= tptp.hoaslaminj (forall @t105 (=> @t104 (forall (@list @t93) (=> (forall @t101 (= (_ (_ tptp.sub @t94) @t18) (_ (_ @t93 @t19) @t34))) (=> (= @t100 (_ @t99 (lambda @t98 @t94))) (forall @t98 (= @t97 @t94))))))))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.39/0.73 (assume @p63 (= tptp.hoaslamnotap (forall @t105 (=> @t104 (forall @t51 (not (= (_ @t99 (lambda (@list @t1 @t47) (_ @t96 @t47))) @t106))))))) % 0.39/0.73 (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))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.39/0.73 (assume @p66 (= tptp.hoaslamnotvar (forall @t105 (=> @t104 (not (_ (_ @t107 @t100) tptp.id)))))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.39/0.73 (assume @p69 (= tptp.hoasapnotvar (forall @t51 (not (_ (_ @t107 @t106) tptp.id))))) % 0.39/0.73 (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))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.39/0.73 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t110 (exists @t58 @t109)))) % 0.39/0.73 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.39/0.73 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t120 (=> @t119 (=> @t118 (=> @t114 (=> @t109 (forall @t13 (=> @t39 @t111))))))))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t120 (=> @t119 (=> @t118 (=> @t122 (=> @t109 (forall @t51 (=> @t111 (=> @t84 (_ @t56 @t9))))))))))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t73 (exists @t105 (forall @t12 (= @t97 @t82)))))) % 0.39/0.73 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.39/0.73 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t120 (=> @t119 (=> @t118 @t125))))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.39/0.73 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t120 @t125))) % 0.39/0.73 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.39/0.73 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t110 (=> @t119 (=> @t118 (=> @t114 (forall @t13 (=> @t39 @t113)))))))) % 0.39/0.73 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t126)) % 0.39/0.73 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t126)) % 0.39/0.73 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t110 (=> @t119 (=> @t118 (=> @t122 (forall @t51 (=> @t113 (=> @t121 (_ (_ @t112 @t9) tptp.id)))))))))) % 0.39/0.73 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t127)) % 0.39/0.73 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t127)) % 0.39/0.73 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t110 (=> @t124 @t129)))) % 0.39/0.73 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.39/0.73 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t110 (=> (forall @t105 (=> (exists @t69 (forall @t101 (and (= @t103 (_ (_ tptp.sub (_ @t63 @t10)) @t18)) (= (_ @t63 @t35) @t102)))) @t123)) @t129)))) % 0.39/0.73 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t110 (=> @t119 (=> @t118 @t130))))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.39/0.73 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t110 @t130))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.39/0.73 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t73 (exists @t105 (= (_ @t3 @t37) @t131))))) % 0.39/0.73 (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)))))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.39/0.73 (assume @p103 (= tptp.hoasinduction (forall @t110 (=> @t119 (=> @t118 (=> @t114 @t132)))))) % 0.39/0.73 (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 @t133)))))))))))))))))))))))))))))))))))) % 0.39/0.73 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t133))) % 0.39/0.73 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.39/0.73 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t110 @t132))) % 0.39/0.73 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.39/0.73 (assume @p109 @t134) % 0.39/0.73 (assume @p110 true) % 0.39/0.73 (step @p111 (= tptp.pushprop_p_and_p_prime @t144) :rule refl :args (@t144)) % 0.39/0.73 (step @p112 (= tptp.hoasap @t145) :rule refl :args (@t145)) % 0.39/0.73 (step @p113 (= tptp.hoaslam @t146) :rule refl :args (@t146)) % 0.39/0.73 (step @p114 (= tptp.hoasvar @t147) :rule refl :args (@t147)) % 0.39/0.73 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t148) :rule refl :args (@t148)) % 0.39/0.73 (step @p116 :rule evaluate :args ((= true false))) % 0.39/0.73 (step @p117 :rule aci_norm :args ((= @t167 @t165))) % 0.39/0.73 (step @p118 :rule cong :premises (@p117) :args (@t169)) % 0.39/0.73 (step @p119 :rule quant-merge-prenex :args ((= (forall @t62 @t171) @t169))) % 0.39/0.73 (step @p120 :rule alpha_equiv :args (@t172 (@list @t149) (@list @t47))) % 0.39/0.73 (step @p121 :rule refl :args (@t158)) % 0.39/0.73 (step @p122 :rule refl :args (@t164)) % 0.39/0.73 (step @p123 :rule nary_cong :premises (@p122 @p121 @p120) :args (@t173)) % 0.39/0.73 (step @p124 :rule quant-miniscope-or :args ((= @t171 @t173))) % 0.39/0.73 (step @p125 :rule trans :premises (@p124 @p123)) % 0.39/0.73 (step @p126 :rule symm :premises (@p125)) % 0.39/0.73 (step @p127 :rule cong :premises (@p126) :args ((forall @t62 @t179))) % 0.39/0.73 (step @p128 :rule trans :premises (@p127 @p119)) % 0.39/0.73 (step @p129 :rule trans :premises (@p128 @p118)) % 0.39/0.73 (step @p130 :rule aci_norm :args ((= (or @t164 (or @t158 @t178)) @t179))) % 0.39/0.73 (step @p131 :rule bool-impl-elim :args (@t157 @t178)) % 0.39/0.73 (step @p132 :rule nary_cong :premises (@p122 @p131) :args ((or @t164 @t180))) % 0.39/0.73 (step @p133 :rule trans :premises (@p132 @p130)) % 0.39/0.73 (step @p134 :rule bool-impl-elim :args (@t163 @t180)) % 0.39/0.73 (step @p135 :rule trans :premises (@p134 @p133)) % 0.39/0.73 (step @p136 :rule cong :premises (@p135) :args ((forall @t62 (=> @t163 @t180)))) % 0.39/0.73 (step @p137 :rule trans :premises (@p136 @p129)) % 0.39/0.73 (step @p138 :rule refl :args ((_ @t56 @t64))) % 0.39/0.73 (step @p139 :rule refl :args (@t174)) % 0.39/0.73 (step @p140 :rule cong :premises (@p139) :args (@t175)) % 0.39/0.73 (step @p141 :rule trans :premises (@p140 @p138)) % 0.39/0.73 (step @p142 :rule refl :args (@t56)) % 0.39/0.73 (step @p143 :rule ho_cong :premises (@p142 @p139)) % 0.39/0.73 (step @p144 :rule cong :premises (@p143 @p141) :args ((= (_ @t56 @t174) @t175))) % 0.39/0.73 (step @p145 :rule symm :premises (@p144)) % 0.39/0.73 (step @p146 :rule refl :args (@t65)) % 0.39/0.73 (step @p147 :rule eq_resolve :premises (@p146 @p145)) % 0.39/0.73 (step @p148 :rule refl :args (@t64)) % 0.39/0.73 (step @p149 :rule cong :premises (@p148 @p139) :args ((= @t64 @t174))) % 0.39/0.73 (step @p150 :rule symm :premises (@p149)) % 0.39/0.73 (step @p151 :rule eq_resolve :premises (@p148 @p150)) % 0.39/0.73 (step @p152 :rule ho_cong :premises (@p142 @p151)) % 0.39/0.73 (step @p153 :rule trans :premises (@p152 @p147)) % 0.39/0.73 (step @p154 :rule refl :args (@t176)) % 0.39/0.73 (step @p155 :rule refl :args (@t66)) % 0.39/0.73 (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t66 @t176))) % 0.39/0.73 (step @p157 :rule symm :premises (@p156)) % 0.39/0.73 (step @p158 :rule eq_resolve :premises (@p155 @p157)) % 0.39/0.73 (step @p159 :rule cong :premises (@p158) :args (@t181)) % 0.39/0.73 (step @p160 :rule refl :args (@t177)) % 0.39/0.73 (step @p161 :rule refl :args (@t68)) % 0.39/0.73 (step @p162 :rule cong :premises (@p161 @p160) :args ((= @t68 @t177))) % 0.39/0.73 (step @p163 :rule symm :premises (@p162)) % 0.39/0.73 (step @p164 :rule eq_resolve :premises (@p161 @p163)) % 0.39/0.73 (step @p165 :rule cong :premises (@p164) :args (@t182)) % 0.39/0.73 (step @p166 :rule nary_cong :premises (@p165 @p159 @p153) :args (@t183)) % 0.39/0.73 (step @p167 :rule cong :premises (@p166) :args ((forall @t69 @t183))) % 0.39/0.73 (step @p168 :rule aci_norm :args ((= (or @t182 (or @t181 @t65)) @t183))) % 0.39/0.73 (step @p169 :rule bool-impl-elim :args (@t66 @t65)) % 0.39/0.73 (step @p170 :rule refl :args (@t182)) % 0.39/0.73 (step @p171 :rule nary_cong :premises (@p170 @p169) :args ((or @t182 @t67))) % 0.39/0.73 (step @p172 :rule trans :premises (@p171 @p168)) % 0.39/0.73 (step @p173 :rule bool-impl-elim :args (@t68 @t67)) % 0.39/0.73 (step @p174 :rule trans :premises (@p173 @p172)) % 0.39/0.73 (step @p175 :rule cong :premises (@p174) :args (@t70)) % 0.39/0.73 (step @p176 :rule trans :premises (@p175 @p167)) % 0.39/0.73 (step @p177 :rule refl :args ((_ @t40 @t4))) % 0.39/0.73 (step @p178 :rule refl :args (@t153)) % 0.39/0.73 (step @p179 :rule cong :premises (@p178) :args (@t154)) % 0.39/0.73 (step @p180 :rule trans :premises (@p179 @p177)) % 0.39/0.73 (step @p181 :rule refl :args (@t40)) % 0.39/0.73 (step @p182 :rule ho_cong :premises (@p181 @p178)) % 0.39/0.73 (step @p183 :rule cong :premises (@p182 @p180) :args ((= (_ @t40 @t153) @t154))) % 0.39/0.73 (step @p184 :rule symm :premises (@p183)) % 0.39/0.73 (step @p185 :rule refl :args (@t71)) % 0.39/0.73 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.39/0.73 (step @p187 :rule refl :args (@t4)) % 0.39/0.73 (step @p188 :rule cong :premises (@p187 @p178) :args ((= @t4 @t153))) % 0.39/0.73 (step @p189 :rule symm :premises (@p188)) % 0.39/0.73 (step @p190 :rule eq_resolve :premises (@p187 @p189)) % 0.39/0.73 (step @p191 :rule ho_cong :premises (@p181 @p190)) % 0.39/0.73 (step @p192 :rule trans :premises (@p191 @p186)) % 0.39/0.73 (step @p193 :rule refl :args (@t155)) % 0.39/0.73 (step @p194 :rule refl :args (@t72)) % 0.39/0.73 (step @p195 :rule cong :premises (@p194 @p193) :args ((= @t72 @t155))) % 0.39/0.73 (step @p196 :rule symm :premises (@p195)) % 0.39/0.73 (step @p197 :rule eq_resolve :premises (@p194 @p196)) % 0.39/0.73 (step @p198 :rule cong :premises (@p197) :args (@t184)) % 0.39/0.73 (step @p199 :rule nary_cong :premises (@p198 @p192) :args (@t185)) % 0.39/0.73 (step @p200 :rule cong :premises (@p199) :args ((forall @t73 @t185))) % 0.39/0.73 (step @p201 :rule bool-impl-elim :args (@t72 @t71)) % 0.39/0.73 (step @p202 :rule cong :premises (@p201) :args (@t74)) % 0.39/0.73 (step @p203 :rule trans :premises (@p202 @p200)) % 0.39/0.73 (step @p204 :rule cong :premises (@p203 @p176) :args (@t75)) % 0.39/0.73 (step @p205 :rule beta-reduce :args ((= (_ @t186 @t56) @t163))) % 0.39/0.73 (step @p206 :rule refl :args (@t56)) % 0.39/0.73 (step @p207 :rule beta-reduce :args ((= (_ @t187 @t40) @t186))) % 0.39/0.73 (step @p208 :rule refl :args (@t40)) % 0.39/0.73 (step @p209 :rule beta-reduce :args ((= (_ @t188 @t1) @t187))) % 0.39/0.73 (step @p210 :rule refl :args (@t1)) % 0.39/0.73 (step @p211 :rule beta-reduce :args ((= @t189 @t188))) % 0.39/0.73 (step @p212 :rule ho_cong :premises (@p211 @p210)) % 0.39/0.73 (step @p213 :rule trans :premises (@p212 @p209)) % 0.39/0.73 (step @p214 :rule ho_cong :premises (@p213 @p208)) % 0.39/0.73 (step @p215 :rule trans :premises (@p214 @p207)) % 0.39/0.73 (step @p216 :rule ho_cong :premises (@p215 @p206)) % 0.39/0.73 (step @p217 :rule trans :premises (@p216 @p205)) % 0.39/0.73 (step @p218 :rule cong :premises (@p217 @p204) :args (@t190)) % 0.39/0.73 (step @p219 :rule cong :premises (@p218) :args (@t191)) % 0.39/0.73 (step @p220 :rule trans :premises (@p219 @p137)) % 0.39/0.73 (step @p221 :rule refl :args (tptp.pushprop_lem2v2)) % 0.39/0.73 (step @p222 :rule cong :premises (@p221 @p220) :args ((= tptp.pushprop_lem2v2 @t191))) % 0.39/0.73 (step @p223 :rule refl :args (@t75)) % 0.39/0.73 (step @p224 :rule refl :args (@t5)) % 0.39/0.73 (step @p225 :rule refl :args ((_ @t40 @t137))) % 0.39/0.73 (step @p226 :rule refl :args ((tptp.sub @t135 @t10))) % 0.39/0.73 (step @p227 :rule refl :args (@t159)) % 0.39/0.73 (step @p228 :rule refl :args (@t135)) % 0.39/0.73 (step @p229 :rule cong :premises (@p228 @p227) :args (@t160)) % 0.39/0.73 (step @p230 :rule trans :premises (@p229 @p226)) % 0.39/0.73 (step @p231 :rule cong :premises (@p230) :args (@t161)) % 0.39/0.73 (step @p232 :rule trans :premises (@p231 @p225)) % 0.39/0.73 (step @p233 :rule ho_cong :premises (@p181 @p230)) % 0.39/0.73 (step @p234 :rule cong :premises (@p233 @p232) :args ((= (_ @t40 @t160) @t161))) % 0.39/0.73 (step @p235 :rule symm :premises (@p234)) % 0.39/0.73 (step @p236 :rule refl :args (@t138)) % 0.39/0.73 (step @p237 :rule eq_resolve :premises (@p236 @p235)) % 0.39/0.73 (step @p238 :rule refl :args (@t136)) % 0.39/0.73 (step @p239 :rule ho_cong :premises (@p238 @p227)) % 0.39/0.73 (step @p240 :rule cong :premises (@p239 @p230) :args ((= (_ @t136 @t159) @t160))) % 0.39/0.73 (step @p241 :rule symm :premises (@p240)) % 0.39/0.73 (step @p242 :rule refl :args (@t137)) % 0.39/0.73 (step @p243 :rule eq_resolve :premises (@p242 @p241)) % 0.39/0.73 (step @p244 :rule refl :args (@t10)) % 0.39/0.73 (step @p245 :rule cong :premises (@p244 @p227) :args ((= @t10 @t159))) % 0.39/0.73 (step @p246 :rule symm :premises (@p245)) % 0.39/0.73 (step @p247 :rule eq_resolve :premises (@p244 @p246)) % 0.39/0.73 (step @p248 :rule ho_cong :premises (@p238 @p247)) % 0.39/0.73 (step @p249 :rule trans :premises (@p248 @p243)) % 0.39/0.73 (step @p250 :rule ho_cong :premises (@p181 @p249)) % 0.39/0.73 (step @p251 :rule trans :premises (@p250 @p237)) % 0.39/0.73 (step @p252 :rule refl :args (@t162)) % 0.39/0.73 (step @p253 :rule refl :args (@t139)) % 0.39/0.73 (step @p254 :rule cong :premises (@p253 @p252) :args ((= @t139 @t162))) % 0.39/0.73 (step @p255 :rule symm :premises (@p254)) % 0.39/0.73 (step @p256 :rule eq_resolve :premises (@p253 @p255)) % 0.39/0.73 (step @p257 :rule cong :premises (@p256 @p251) :args (@t140)) % 0.39/0.73 (step @p258 :rule cong :premises (@p257) :args (@t142)) % 0.39/0.73 (step @p259 :rule cong :premises (@p258) :args (@t144)) % 0.39/0.73 (step @p260 :rule trans :premises (@p111 @p259)) % 0.39/0.73 (step @p261 :rule ho_cong :premises (@p260 @p224)) % 0.39/0.73 (step @p262 :rule ho_cong :premises (@p261 @p210)) % 0.39/0.73 (step @p263 :rule ho_cong :premises (@p262 @p208)) % 0.39/0.73 (step @p264 :rule ho_cong :premises (@p263 @p206)) % 0.39/0.73 (step @p265 :rule cong :premises (@p264 @p223) :args (@t76)) % 0.39/0.73 (step @p266 :rule cong :premises (@p265) :args (@t77)) % 0.39/0.73 (step @p267 :rule cong :premises (@p221 @p266) :args (@t78)) % 0.39/0.73 (step @p268 :rule trans :premises (@p267 @p222)) % 0.39/0.73 (step @p269 :rule eq_resolve :premises (@p33 @p268)) % 0.39/0.73 (step @p270 :rule refl :args ((tptp.comp tptp.sh @t10))) % 0.39/0.73 (step @p271 :rule refl :args (tptp.sh)) % 0.39/0.73 (step @p272 :rule cong :premises (@p271 @p227) :args (@t192)) % 0.39/0.73 (step @p273 :rule trans :premises (@p272 @p270)) % 0.39/0.73 (step @p274 :rule refl :args (@t28)) % 0.39/0.73 (step @p275 :rule ho_cong :premises (@p274 @p227)) % 0.39/0.73 (step @p276 :rule cong :premises (@p275 @p273) :args ((= (_ @t28 @t159) @t192))) % 0.39/0.73 (step @p277 :rule symm :premises (@p276)) % 0.39/0.73 (step @p278 :rule refl :args (@t29)) % 0.39/0.73 (step @p279 :rule eq_resolve :premises (@p278 @p277)) % 0.39/0.73 (step @p280 :rule ho_cong :premises (@p274 @p247)) % 0.39/0.73 (step @p281 :rule trans :premises (@p280 @p279)) % 0.39/0.73 (step @p282 :rule refl :args (@t1)) % 0.39/0.73 (step @p283 :rule cong :premises (@p282 @p281) :args (@t193)) % 0.39/0.73 (step @p284 :rule cong :premises (@p283) :args ((forall @t12 @t193))) % 0.39/0.73 (step @p285 :rule eq-symm :args (@t29 @t1)) % 0.39/0.73 (step @p286 :rule cong :premises (@p285) :args (@t30)) % 0.39/0.73 (step @p287 :rule trans :premises (@p286 @p284)) % 0.39/0.73 (step @p288 :rule refl :args (tptp.axshiftcons)) % 0.39/0.73 (step @p289 :rule cong :premises (@p288 @p287) :args (@t31)) % 0.39/0.73 (step @p290 :rule eq_resolve :premises (@p7 @p289)) % 0.39/0.73 (step @p291 :rule cong :premises (@p290 @p269) :args (@t79)) % 0.39/0.73 (step @p292 :rule refl :args ((tptp.sub @t5 @t19))) % 0.39/0.73 (step @p293 :rule refl :args (@t194)) % 0.39/0.73 (step @p294 :rule refl :args (@t5)) % 0.39/0.73 (step @p295 :rule cong :premises (@p294 @p293) :args (@t195)) % 0.39/0.73 (step @p296 :rule trans :premises (@p295 @p292)) % 0.39/0.73 (step @p297 :rule refl :args (@t6)) % 0.39/0.73 (step @p298 :rule ho_cong :premises (@p297 @p293)) % 0.39/0.73 (step @p299 :rule cong :premises (@p298 @p296) :args ((= (_ @t6 @t194) @t195))) % 0.39/0.73 (step @p300 :rule symm :premises (@p299)) % 0.39/0.73 (step @p301 :rule refl :args (@t20)) % 0.39/0.73 (step @p302 :rule eq_resolve :premises (@p301 @p300)) % 0.39/0.73 (step @p303 :rule refl :args (@t19)) % 0.39/0.73 (step @p304 :rule cong :premises (@p303 @p293) :args ((= @t19 @t194))) % 0.39/0.73 (step @p305 :rule symm :premises (@p304)) % 0.39/0.73 (step @p306 :rule eq_resolve :premises (@p303 @p305)) % 0.39/0.73 (step @p307 :rule ho_cong :premises (@p297 @p306)) % 0.39/0.73 (step @p308 :rule trans :premises (@p307 @p302)) % 0.39/0.73 (step @p309 :rule refl :args ((tptp.sub @t7 @t18))) % 0.39/0.73 (step @p310 :rule refl :args (@t18)) % 0.39/0.73 (step @p311 :rule refl :args (@t196)) % 0.39/0.73 (step @p312 :rule cong :premises (@p311 @p310) :args (@t197)) % 0.39/0.73 (step @p313 :rule trans :premises (@p312 @p309)) % 0.39/0.73 (step @p314 :rule refl :args (tptp.sub)) % 0.39/0.73 (step @p315 :rule ho_cong :premises (@p314 @p311)) % 0.39/0.73 (step @p316 :rule ho_cong :premises (@p315 @p310)) % 0.39/0.73 (step @p317 :rule cong :premises (@p316 @p313) :args ((= (_ (_ tptp.sub @t196) @t18) @t197))) % 0.39/0.73 (step @p318 :rule symm :premises (@p317)) % 0.39/0.73 (step @p319 :rule refl :args (@t21)) % 0.39/0.73 (step @p320 :rule eq_resolve :premises (@p319 @p318)) % 0.39/0.73 (step @p321 :rule refl :args (@t7)) % 0.39/0.73 (step @p322 :rule cong :premises (@p321 @p311) :args ((= @t7 @t196))) % 0.39/0.73 (step @p323 :rule symm :premises (@p322)) % 0.39/0.73 (step @p324 :rule eq_resolve :premises (@p321 @p323)) % 0.39/0.73 (step @p325 :rule ho_cong :premises (@p314 @p324)) % 0.39/0.73 (step @p326 :rule ho_cong :premises (@p325 @p310)) % 0.39/0.73 (step @p327 :rule trans :premises (@p326 @p320)) % 0.39/0.73 (step @p328 :rule cong :premises (@p327 @p308) :args (@t22)) % 0.39/0.73 (step @p329 :rule cong :premises (@p328) :args (@t24)) % 0.39/0.73 (step @p330 :rule refl :args (tptp.axclos)) % 0.39/0.73 (step @p331 :rule cong :premises (@p330 @p329) :args (@t25)) % 0.39/0.73 (step @p332 :rule eq_resolve :premises (@p5 @p331)) % 0.39/0.73 (step @p333 :rule cong :premises (@p332 @p291) :args (@t80)) % 0.39/0.73 (step @p334 :rule refl :args (tptp.pushprop_lem2v2_lthm)) % 0.39/0.73 (step @p335 :rule cong :premises (@p334 @p333) :args (@t81)) % 0.39/0.73 (step @p336 :rule eq_resolve :premises (@p35 @p335)) % 0.39/0.73 (step @p337 :rule cong :premises (@p336) :args (@t134)) % 0.39/0.73 (step @p338 :rule eq_resolve :premises (@p109 @p337)) % 0.39/0.73 (step @p339 :rule not_implies_elim2 :premises (@p338)) % 0.39/0.73 (step @p340 :rule not_implies_elim2 :premises (@p339)) % 0.39/0.73 (step @p341 :rule skolemize :premises (@p340)) % 0.39/0.73 (step @p342 :rule bool-double-not-elim :args (@t204)) % 0.39/0.73 (step @p343 :rule refl :args (@t213)) % 0.39/0.73 (step @p344 :rule nary_cong :premises (@p343 @p342) :args ((or @t213 (not @t212)))) % 0.39/0.73 (step @p345 :rule cnf_or_neg :args (@t213 0)) % 0.39/0.73 (step @p346 :rule eq_resolve :premises (@p345 @p344)) % 0.39/0.73 (step @p347 :rule reordering :premises (@p346) :args ((or @t204 @t213))) % 0.39/0.73 (step @p348 :rule chain_m_resolution :premises (@p347 @p341) :args (@t204 @t214 @t215)) % 0.39/0.73 (step @p349 :rule instantiate :premises (@p348) :args ((@list @t206))) % 0.39/0.73 (step @p350 :rule cnf_or_neg :args (@t213 4)) % 0.39/0.73 (step @p351 :rule chain_m_resolution :premises (@p350 @p341) :args ((not @t207) @t214 @t215)) % 0.39/0.73 (step @p352 :rule cnf_equiv_pos2 :args (@t217)) % 0.39/0.73 (step @p353 :rule reordering :premises (@p352) :args ((or @t207 @t218 (not @t217)))) % 0.39/0.73 (step @p354 :rule chain_m_resolution :premises (@p353 @p351 @p349) :args (@t218 (@list true false) (@list @t207 @t217))) % 0.39/0.73 (step @p355 :rule false_intro :premises (@p354)) % 0.39/0.73 (step @p356 :rule not_implies_elim1 :premises (@p338)) % 0.39/0.73 (step @p357 :rule instantiate :premises (@p356) :args ((@list @t205 tptp.sh @t201))) % 0.39/0.73 (step @p358 :rule symm :premises (@p357)) % 0.39/0.73 (step @p359 :rule not_implies_elim1 :premises (@p339)) % 0.39/0.73 (step @p360 :rule instantiate :premises (@p359) :args ((@list @t200 @t199))) % 0.39/0.73 (step @p361 :rule refl :args (@t205)) % 0.39/0.73 (step @p362 :rule cong :premises (@p361 @p360) :args (@t219)) % 0.39/0.73 (step @p363 :rule trans :premises (@p362 @p358)) % 0.39/0.73 (step @p364 :rule cong :premises (@p363) :args (@t220)) % 0.39/0.73 (step @p365 :rule bool-double-not-elim :args (@t210)) % 0.39/0.73 (step @p366 :rule nary_cong :premises (@p343 @p365) :args ((or @t213 (not @t211)))) % 0.39/0.73 (step @p367 :rule cnf_or_neg :args (@t213 1)) % 0.39/0.73 (step @p368 :rule eq_resolve :premises (@p367 @p366)) % 0.39/0.73 (step @p369 :rule reordering :premises (@p368) :args ((or @t210 @t213))) % 0.39/0.73 (step @p370 :rule chain_m_resolution :premises (@p369 @p341) :args (@t210 @t214 @t215)) % 0.39/0.73 (step @p371 :rule instantiate :premises (@p370) :args ((@list @t205))) % 0.39/0.73 (step @p372 :rule bool-double-not-elim :args (@t208)) % 0.39/0.73 (step @p373 :rule nary_cong :premises (@p343 @p372) :args ((or @t213 (not @t209)))) % 0.39/0.73 (step @p374 :rule cnf_or_neg :args (@t213 2)) % 0.39/0.73 (step @p375 :rule eq_resolve :premises (@p374 @p373)) % 0.39/0.73 (step @p376 :rule reordering :premises (@p375) :args ((or @t208 @t213))) % 0.39/0.73 (step @p377 :rule chain_m_resolution :premises (@p376 @p341) :args (@t208 @t214 @t215)) % 0.39/0.73 (step @p378 :rule cnf_or_pos :args (@t221)) % 0.39/0.73 (step @p379 :rule reordering :premises (@p378) :args ((or @t209 @t220 (not @t221)))) % 0.39/0.73 (step @p380 :rule chain_m_resolution :premises (@p379 @p377 @p371) :args (@t220 (@list false false) (@list @t208 @t221))) % 0.39/0.73 (step @p381 :rule true_intro :premises (@p380)) % 0.39/0.73 (step @p382 :rule symm :premises (@p381)) % 0.39/0.73 (step @p383 :rule trans :premises (@p382 @p364 @p355)) % 0.39/0.73 (step @p384 false :rule eq_resolve :premises (@p383 @p116)) % 0.39/0.73 ) % 0.39/0.73 % SZS output end Proof % 0.39/0.73 % cvc5 exiting %------------------------------------------------------------------------------