%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG259^2 : 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 : n024.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:05:40 AM UTC 2026 % Result : Theorem 0.26s 0.46s % Output : Proof 0.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : ALG259^2 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n024.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 20:55:00 EDT 2026 % 0.08/0.25 % CPUTime : % 0.16/0.36 %----Proving TH0 % 0.26/0.46 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.26/0.46 % SZS status Theorem % 0.26/0.46 % SZS output start Proof % 0.26/0.46 ( % 0.26/0.46 (declare-sort tptp.term 0) % 0.26/0.46 (declare-sort tptp.subst 0) % 0.26/0.46 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.26/0.46 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.26/0.46 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.26/0.46 (declare-const tptp.one tptp.term) % 0.26/0.46 (declare-const tptp.sh tptp.subst) % 0.26/0.46 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.26/0.46 (declare-const tptp.var (-> tptp.term Bool)) % 0.26/0.46 (declare-const tptp.id tptp.subst) % 0.26/0.46 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3b Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3a Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3 Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem2 Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem1 Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasinduction_lem0 Bool) % 0.26/0.46 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasapnotvar Bool) % 0.26/0.46 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.26/0.46 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.26/0.46 (declare-const tptp.hoaslamnotvar Bool) % 0.26/0.46 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.26/0.46 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.26/0.46 (declare-const tptp.hoaslamnotap Bool) % 0.26/0.46 (declare-const tptp.hoaslaminj_lthm Bool) % 0.26/0.46 (declare-const tptp.hoaslaminj_gthm Bool) % 0.26/0.46 (declare-const tptp.hoaslaminj Bool) % 0.26/0.46 (declare-const tptp.hoasapinj2_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasapinj2_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasapinj2 Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.26/0.46 (declare-const tptp.axassoc Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.26/0.46 (declare-const tptp.axvarcons Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem0 Bool) % 0.26/0.46 (declare-const tptp.apinj1 Bool) % 0.26/0.46 (declare-const tptp.induction Bool) % 0.26/0.46 (declare-const tptp.apnotvar Bool) % 0.26/0.46 (declare-const tptp.laminj Bool) % 0.26/0.46 (declare-const tptp.axvarshift Bool) % 0.26/0.46 (declare-const tptp.ulamvarind Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.26/0.46 (declare-const tptp.ulamvarsh Bool) % 0.26/0.46 (declare-const tptp.ulamvar1 Bool) % 0.26/0.46 (declare-const tptp.axabs Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem1 Bool) % 0.26/0.46 (declare-const tptp.shinj Bool) % 0.26/0.46 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.26/0.46 (declare-const tptp.apinj2 Bool) % 0.26/0.46 (declare-const tptp.axvarid Bool) % 0.26/0.46 (declare-const tptp.axidl Bool) % 0.26/0.46 (declare-const tptp.axclos Bool) % 0.26/0.46 (declare-const tptp.termmset Bool) % 0.26/0.46 (declare-const tptp.axshiftcons Bool) % 0.26/0.46 (declare-const tptp.lamnotap Bool) % 0.26/0.46 (declare-const tptp.lamnotvar Bool) % 0.26/0.46 (declare-const tptp.axapp Bool) % 0.26/0.46 (declare-const tptp.axscons Bool) % 0.26/0.46 (declare-const tptp.axmap Bool) % 0.26/0.46 (declare-const tptp.axidr Bool) % 0.26/0.46 (declare-const tptp.induction2lem Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasapinj1_lthm Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem1v2 Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.26/0.46 (declare-const tptp.induction2 Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem2v2 Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem3v2 Bool) % 0.26/0.46 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.26/0.46 (declare-const tptp.pushprop Bool) % 0.26/0.46 (declare-const tptp.pushprop_gthm Bool) % 0.26/0.46 (declare-const tptp.hoasapinj1 Bool) % 0.26/0.46 (declare-const tptp.pushprop_lthm_orig Bool) % 0.26/0.46 (declare-const tptp.pushprop_lthm Bool) % 0.26/0.46 (declare-const tptp.induction2lem_gthm Bool) % 0.26/0.46 (declare-const tptp.induction2lem_lthm Bool) % 0.26/0.46 (declare-const tptp.induction2_gthm Bool) % 0.26/0.46 (declare-const tptp.induction2_lthm Bool) % 0.26/0.46 (declare-const tptp.substmonoid Bool) % 0.26/0.46 (declare-const tptp.substmonoid_gthm Bool) % 0.26/0.46 (declare-const tptp.termmset_gthm Bool) % 0.26/0.46 (declare-const tptp.substmonoid_lthm Bool) % 0.26/0.46 (declare-const tptp.termmset_lthm Bool) % 0.26/0.46 (declare-const tptp.hoasapinj1_gthm Bool) % 0.26/0.46 (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)))))))))))) % 0.26/0.46 (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)))))) % 0.26/0.46 (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))))) % 0.26/0.46 (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)))))) % 0.26/0.46 (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)))))))) % 0.26/0.46 (define @t1 () (@var "M" tptp.subst)) % 0.26/0.46 (define @t2 () (@var "B" tptp.term)) % 0.26/0.46 (define @t3 () (_ tptp.sub @t2)) % 0.26/0.46 (define @t4 () (_ @t3 @t1)) % 0.26/0.46 (define @t5 () (@var "A" tptp.term)) % 0.26/0.46 (define @t6 () (_ tptp.sub @t5)) % 0.26/0.46 (define @t7 () (_ @t6 @t1)) % 0.26/0.46 (define @t8 () (_ tptp.ap @t5)) % 0.26/0.46 (define @t9 () (_ @t8 @t2)) % 0.26/0.46 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.26/0.46 (define @t11 () (_ tptp.sub tptp.one)) % 0.26/0.46 (define @t12 () (@list @t5 @t1)) % 0.26/0.46 (define @t13 () (_ @t6 tptp.id)) % 0.26/0.46 (define @t14 () (@list @t5)) % 0.26/0.46 (define @t15 () (forall @t14 (= @t13 @t5))) % 0.26/0.46 (define @t16 () (_ tptp.comp @t1)) % 0.26/0.46 (define @t17 () (_ tptp.push tptp.one)) % 0.26/0.46 (define @t18 () (_ tptp.lam @t5)) % 0.26/0.46 (define @t19 () (@var "N" tptp.subst)) % 0.26/0.46 (define @t20 () (_ @t16 @t19)) % 0.26/0.46 (define @t21 () (@list @t5 @t1 @t19)) % 0.26/0.46 (define @t22 () (forall @t21 (= (_ (_ tptp.sub @t7) @t19) (_ @t6 @t20)))) % 0.26/0.46 (define @t23 () (@list @t1)) % 0.26/0.46 (define @t24 () (forall @t23 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 0.26/0.46 (define @t25 () (_ tptp.comp tptp.sh)) % 0.26/0.46 (define @t26 () (@var "K" tptp.subst)) % 0.26/0.46 (define @t27 () (forall (@list @t1 @t19 @t26) (= (_ (_ tptp.comp @t20) @t26) (_ @t16 (_ (_ tptp.comp @t19) @t26))))) % 0.26/0.46 (define @t28 () (_ @t6 @t19)) % 0.26/0.46 (define @t29 () (_ (_ tptp.push @t28) @t20)) % 0.26/0.46 (define @t30 () (forall @t23 (= (_ @t16 tptp.id) @t1))) % 0.26/0.46 (define @t31 () (_ @t17 tptp.sh)) % 0.26/0.46 (define @t32 () (_ @t6 tptp.sh)) % 0.26/0.46 (define @t33 () (_ tptp.var @t5)) % 0.26/0.46 (define @t34 () (@var "P" (-> tptp.term Bool))) % 0.26/0.46 (define @t35 () (_ @t34 @t5)) % 0.26/0.46 (define @t36 () (forall @t14 (=> @t33 @t35))) % 0.26/0.46 (define @t37 () (@list @t34)) % 0.26/0.46 (define @t38 () (= @t5 @t2)) % 0.26/0.46 (define @t39 () (@var "D" tptp.term)) % 0.26/0.46 (define @t40 () (_ tptp.ap @t2)) % 0.26/0.46 (define @t41 () (@var "C" tptp.term)) % 0.26/0.46 (define @t42 () (= (_ @t8 @t41) (_ @t40 @t39))) % 0.26/0.46 (define @t43 () (@list @t5 @t2 @t41 @t39)) % 0.26/0.46 (define @t44 () (= @t41 @t39)) % 0.26/0.46 (define @t45 () (@list @t5 @t2)) % 0.26/0.46 (define @t46 () (_ @t40 @t41)) % 0.26/0.46 (define @t47 () (= @t18 @t46)) % 0.26/0.46 (define @t48 () (not @t47)) % 0.26/0.46 (define @t49 () (@list @t5 @t2 @t41)) % 0.26/0.46 (define @t50 () (forall @t49 @t48)) % 0.26/0.46 (define @t51 () (= tptp.lamnotap @t50)) % 0.26/0.46 (define @t52 () (forall @t14 @t35)) % 0.26/0.46 (define @t53 () (_ @t34 @t18)) % 0.26/0.46 (define @t54 () (_ @t34 @t2)) % 0.26/0.46 (define @t55 () (forall @t45 (=> @t35 (=> @t54 (_ @t34 @t9))))) % 0.26/0.46 (define @t56 () (@var "Q" (-> tptp.term Bool))) % 0.26/0.46 (define @t57 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t34) @t56)) % 0.26/0.46 (define @t58 () (@list @t56)) % 0.26/0.46 (define @t59 () (@list @t34 @t5 @t1)) % 0.26/0.46 (define @t60 () (_ tptp.push @t2)) % 0.26/0.46 (define @t61 () (@var "K" (-> tptp.term Bool))) % 0.26/0.46 (define @t62 () (@list @t34 @t56 @t5 @t1)) % 0.26/0.46 (define @t63 () (_ tptp.sub @t41)) % 0.26/0.46 (define @t64 () (@list @t41)) % 0.26/0.46 (define @t65 () (_ tptp.var @t2)) % 0.26/0.46 (define @t66 () (@list @t2)) % 0.26/0.46 (define @t67 () (forall @t66 (=> @t65 (_ @t34 @t4)))) % 0.26/0.46 (define @t68 () (_ @t3 @t10)) % 0.26/0.46 (define @t69 () (forall @t66 (=> @t65 (_ @t34 @t68)))) % 0.26/0.46 (define @t70 () (_ @t56 @t2)) % 0.26/0.46 (define @t71 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.26/0.46 (define @t72 () (_ @t6 (_ @t60 tptp.id))) % 0.26/0.46 (define @t73 () (forall @t14 (=> (forall @t66 (=> @t54 (_ @t34 @t72))) @t53))) % 0.26/0.46 (define @t74 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.26/0.46 (define @t75 () (=> tptp.induction2lem tptp.induction2)) % 0.26/0.46 (define @t76 () (_ tptp.hoasap tptp.id)) % 0.26/0.46 (define @t77 () (_ (_ @t76 @t5) tptp.id)) % 0.26/0.46 (define @t78 () (= (_ @t77 @t41) (_ (_ (_ @t76 @t2) tptp.id) @t39))) % 0.26/0.46 (define @t79 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.26/0.46 (define @t80 () (_ (_ @t79 @t1) @t5)) % 0.26/0.46 (define @t81 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.26/0.46 (define @t82 () (_ @t81 @t1)) % 0.26/0.46 (define @t83 () (_ @t82 @t5)) % 0.26/0.46 (define @t84 () (@list @t1 @t5)) % 0.26/0.46 (define @t85 () (_ tptp.hoaslam tptp.id)) % 0.26/0.46 (define @t86 () (_ @t85 (lambda @t84 @t83))) % 0.26/0.46 (define @t87 () (@list @t1 @t5 @t19)) % 0.26/0.46 (define @t88 () (_ (_ @t81 @t20) @t28)) % 0.26/0.46 (define @t89 () (_ (_ tptp.sub @t83) @t19)) % 0.26/0.46 (define @t90 () (= @t89 @t88)) % 0.26/0.46 (define @t91 () (forall @t87 @t90)) % 0.26/0.46 (define @t92 () (@list @t81)) % 0.26/0.46 (define @t93 () (_ @t77 @t2)) % 0.26/0.46 (define @t94 () (lambda (@list @t1 @t41) (_ @t82 @t41))) % 0.26/0.46 (define @t95 () (= (_ @t85 @t94) @t93)) % 0.26/0.46 (define @t96 () (not @t95)) % 0.26/0.46 (define @t97 () (forall @t45 @t96)) % 0.26/0.46 (define @t98 () (=> @t91 @t97)) % 0.26/0.46 (define @t99 () (forall @t92 @t98)) % 0.26/0.46 (define @t100 () (= tptp.hoaslamnotap @t99)) % 0.26/0.46 (define @t101 () (=> tptp.lamnotap tptp.hoaslamnotap)) % 0.26/0.46 (define @t102 () (= tptp.hoaslamnotap_lthm @t101)) % 0.26/0.46 (define @t103 () (_ tptp.hoasvar tptp.id)) % 0.26/0.46 (define @t104 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.26/0.46 (define @t105 () (_ (_ tptp.hoasinduction_p_and_p_prime @t104) @t56)) % 0.26/0.46 (define @t106 () (@list @t104)) % 0.26/0.46 (define @t107 () (_ @t56 @t5)) % 0.26/0.46 (define @t108 () (_ @t104 tptp.id)) % 0.26/0.46 (define @t109 () (_ (_ @t108 @t5) tptp.id)) % 0.26/0.46 (define @t110 () (forall @t14 (=> (_ (_ @t103 @t5) tptp.id) @t109))) % 0.26/0.46 (define @t111 () (_ (_ (_ @t104 @t1) @t5) (_ (_ tptp.comp @t26) @t19))) % 0.26/0.46 (define @t112 () (_ (_ (_ @t104 (_ @t16 @t26)) (_ @t6 @t26)) @t19)) % 0.26/0.46 (define @t113 () (@list @t1 @t5 @t19 @t26)) % 0.26/0.46 (define @t114 () (forall @t113 (=> @t112 @t111))) % 0.26/0.46 (define @t115 () (forall @t113 (=> @t111 @t112))) % 0.26/0.46 (define @t116 () (@list @t104 @t56)) % 0.26/0.46 (define @t117 () (_ (_ @t108 @t2) tptp.id)) % 0.26/0.46 (define @t118 () (forall @t45 (=> @t109 (=> @t117 (_ (_ @t108 @t93) tptp.id))))) % 0.26/0.46 (define @t119 () (=> (forall @t14 (=> @t109 (_ (_ @t108 (_ (_ @t81 tptp.id) @t5)) tptp.id))) (_ (_ @t108 @t86) tptp.id))) % 0.26/0.46 (define @t120 () (forall @t92 (=> @t91 @t119))) % 0.26/0.46 (define @t121 () (=> @t120 (=> @t105 (forall @t14 (=> (forall @t66 (=> @t70 (_ @t56 @t72))) (_ @t56 @t18)))))) % 0.26/0.46 (define @t122 () (=> 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))))))))))))))))))))))))))))))))))) % 0.26/0.46 (define @t123 () (=> 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))))))))))))))))))))))))))))))))))) % 0.26/0.46 (define @t124 () (forall @t66 (=> @t117 (_ (_ @t108 @t72) tptp.id)))) % 0.26/0.46 (define @t125 () (forall @t14 (=> @t124 (_ (_ @t108 (_ tptp.lam (_ @t6 @t31))) tptp.id)))) % 0.26/0.46 (define @t126 () (=> @t120 (forall @t14 (=> @t124 (_ (_ @t108 @t18) tptp.id))))) % 0.26/0.46 (define @t127 () (_ @t81 tptp.sh)) % 0.26/0.46 (define @t128 () (_ @t127 tptp.one)) % 0.26/0.46 (define @t129 () (=> @t118 (=> @t120 (forall @t14 @t109)))) % 0.26/0.46 (define @t130 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.26/0.46 (define @t131 () (not tptp.hoaslamnotap_lthm)) % 0.26/0.46 (define @t132 () (@var "X" tptp.term)) % 0.26/0.46 (define @t133 () (_ @t56 @t132)) % 0.26/0.46 (define @t134 () (@list @t132)) % 0.26/0.46 (define @t135 () (lambda (@list @t5 @t1 @t34 @t56) (forall @t134 (= @t133 (_ @t34 (_ (_ tptp.sub @t132) @t10)))))) % 0.26/0.46 (define @t136 () (_ (_ tptp.ap @t28) @t2)) % 0.26/0.46 (define @t137 () (lambda (@list @t1 @t5 @t19 @t2) @t136)) % 0.26/0.46 (define @t138 () (_ tptp.lam @t128)) % 0.26/0.46 (define @t139 () (lambda (@list @t1 @t81) @t138)) % 0.26/0.46 (define @t140 () (lambda @t87 (_ tptp.var @t28))) % 0.26/0.46 (define @t141 () (lambda @t116 (forall @t134 (= @t133 (_ (_ @t108 @t132) tptp.id))))) % 0.26/0.46 (define @t142 () (@var "BOUND_VARIABLE_9634" tptp.term)) % 0.26/0.46 (define @t143 () (@var "BOUND_VARIABLE_9632" tptp.term)) % 0.26/0.46 (define @t144 () (_ @t81 tptp.sh tptp.one)) % 0.26/0.46 (define @t145 () (tptp.lam @t144)) % 0.26/0.46 (define @t146 () (not (= @t145 (tptp.ap (tptp.sub @t143 tptp.id) @t142)))) % 0.26/0.46 (define @t147 () (tptp.sub @t5 @t19)) % 0.26/0.46 (define @t148 () (tptp.comp @t1 @t19)) % 0.26/0.46 (define @t149 () (_ @t81 @t148 @t147)) % 0.26/0.46 (define @t150 () (_ @t81 @t1 @t5)) % 0.26/0.46 (define @t151 () (tptp.sub @t150 @t19)) % 0.26/0.46 (define @t152 () (forall @t87 (= @t151 @t149))) % 0.26/0.46 (define @t153 () (not @t152)) % 0.26/0.46 (define @t154 () (or @t153 @t146)) % 0.26/0.46 (define @t155 () (forall (@list @t81 @t143 @t142) @t154)) % 0.26/0.46 (define @t156 () (@list @t143 @t142)) % 0.26/0.46 (define @t157 () (forall @t156 @t154)) % 0.26/0.46 (define @t158 () (forall @t156 @t146)) % 0.26/0.46 (define @t159 () (or @t153 @t158)) % 0.26/0.46 (define @t160 () (tptp.sub @t5 tptp.id)) % 0.26/0.46 (define @t161 () (tptp.ap @t160 @t2)) % 0.26/0.46 (define @t162 () (forall @t45 (not (= @t145 @t161)))) % 0.26/0.46 (define @t163 () (_ (_ tptp.ap @t13) @t2)) % 0.26/0.46 (define @t164 () (= @t138 @t163)) % 0.26/0.46 (define @t165 () (not @t164)) % 0.26/0.46 (define @t166 () (lambda @t66 @t163)) % 0.26/0.46 (define @t167 () (lambda (@list @t19 @t2) @t136)) % 0.26/0.46 (define @t168 () (lambda (@list @t5 @t19 @t2) @t136)) % 0.26/0.46 (define @t169 () (_ @t137 tptp.id)) % 0.26/0.46 (define @t170 () (lambda @t64 (_ @t127 @t41))) % 0.26/0.46 (define @t171 () (_ @t94 tptp.sh)) % 0.26/0.46 (define @t172 () (lambda @t92 @t138)) % 0.26/0.46 (define @t173 () (_ @t139 tptp.id)) % 0.26/0.46 (define @t174 () (= (_ @t173 @t94) (_ (_ (_ @t169 @t5) tptp.id) @t2))) % 0.26/0.46 (define @t175 () (not @t174)) % 0.26/0.46 (define @t176 () (forall @t45 @t175)) % 0.26/0.46 (define @t177 () (=> @t91 @t176)) % 0.26/0.46 (define @t178 () (forall @t92 @t177)) % 0.26/0.46 (define @t179 () (tptp.ap @t2 @t41)) % 0.26/0.46 (define @t180 () (tptp.lam @t5)) % 0.26/0.46 (define @t181 () (@quantifiers_skolemize @t155 2)) % 0.26/0.46 (define @t182 () (tptp.sub (@quantifiers_skolemize @t155 1) tptp.id)) % 0.26/0.46 (define @t183 () (@quantifiers_skolemize @t155 0)) % 0.26/0.46 (define @t184 () (_ @t183 tptp.sh tptp.one)) % 0.26/0.46 (define @t185 () (= (tptp.lam @t184) (tptp.ap @t182 @t181))) % 0.26/0.46 (define @t186 () (not @t185)) % 0.26/0.46 (define @t187 () (or (not (forall @t87 (= (tptp.sub (_ @t183 @t1 @t5) @t19) (_ @t183 @t148 @t147)))) @t186)) % 0.26/0.46 (define @t188 () (forall @t49 (not (= @t180 @t179)))) % 0.26/0.46 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.26/0.46 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.26/0.46 (assume @p3 (= tptp.axvarid @t15)) % 0.26/0.46 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t18) @t1) (_ tptp.lam (_ @t6 (_ @t17 (_ @t16 tptp.sh)))))))) % 0.26/0.46 (assume @p5 (= tptp.axclos @t22)) % 0.26/0.46 (assume @p6 (= tptp.axidl @t24)) % 0.26/0.46 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t25 @t10) @t1)))) % 0.26/0.46 (assume @p8 (= tptp.axassoc @t27)) % 0.26/0.46 (assume @p9 (= tptp.axmap (forall @t21 (= (_ (_ tptp.comp @t10) @t19) @t29)))) % 0.26/0.46 (assume @p10 (= tptp.axidr @t30)) % 0.26/0.46 (assume @p11 (= tptp.axvarshift (= @t31 tptp.id))) % 0.26/0.46 (assume @p12 (= tptp.axscons (forall @t23 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t25 @t1)) @t1)))) % 0.26/0.46 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.26/0.46 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t33 (_ tptp.var @t32))))) % 0.26/0.46 (assume @p15 (= tptp.ulamvarind (forall @t37 (=> (_ @t34 tptp.one) (=> (forall @t14 (=> @t33 (=> @t35 (_ @t34 @t32)))) @t36))))) % 0.26/0.46 (assume @p16 (= tptp.apinj1 (forall @t43 (=> @t42 @t38)))) % 0.26/0.46 (assume @p17 (= tptp.apinj2 (forall @t43 (=> @t42 @t44)))) % 0.26/0.46 (assume @p18 (= tptp.laminj (forall @t45 (=> (= @t18 (_ tptp.lam @t2)) @t38)))) % 0.26/0.46 (assume @p19 (= tptp.shinj (forall @t45 (=> (= @t32 (_ @t3 tptp.sh)) @t38)))) % 0.26/0.46 (assume @p20 @t51) % 0.26/0.46 (assume @p21 (= tptp.apnotvar (forall @t45 (not (_ tptp.var @t9))))) % 0.26/0.46 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t18))))) % 0.26/0.46 (assume @p23 (= tptp.induction (forall @t37 (=> @t36 (=> @t55 (=> (forall @t14 (=> @t35 @t53)) @t52)))))) % 0.26/0.46 (assume @p24 (= tptp.pushprop_lem0 (forall @t59 (exists @t58 @t57)))) % 0.26/0.46 (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))))))))))))))))))))))))) % 0.26/0.46 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.26/0.46 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t34 @t61 @t5 @t1 @t2) (=> @t35 (_ @t61 (_ @t6 (_ @t60 @t1))))))) % 0.26/0.46 (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))))))))))))))))))))))))) % 0.26/0.46 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.26/0.46 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t62 (=> @t35 (=> @t57 (_ @t56 tptp.one)))))) % 0.26/0.46 (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))))))))))))))))))))))))) % 0.26/0.46 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.26/0.46 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t62 (=> @t57 (=> @t67 (forall @t64 (=> (_ tptp.var @t41) (=> (_ @t56 @t41) (_ @t56 (_ @t63 tptp.sh)))))))))) % 0.26/0.46 (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))))))))))))))))))))))))) % 0.26/0.46 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.26/0.46 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t62 (=> @t57 (=> (forall @t66 (=> @t65 @t70)) @t69))))) % 0.26/0.46 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.26/0.46 (assume @p38 (= tptp.pushprop (forall @t59 (=> @t67 (=> @t35 @t69))))) % 0.26/0.46 (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))))))))))))))))))))))))) % 0.26/0.46 (assume @p40 (= tptp.pushprop_lthm_orig @t71)) % 0.26/0.46 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t71))) % 0.26/0.46 (assume @p42 (= tptp.induction2lem (forall @t37 (=> @t55 (=> @t73 (forall @t12 (=> @t67 (_ @t34 @t7)))))))) % 0.26/0.46 (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 @t74)))))))))))))))))))))))) % 0.26/0.46 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t74)))))))))) % 0.26/0.46 (assume @p45 (= tptp.induction2 (forall @t37 (=> @t36 (=> @t55 (=> @t73 @t52)))))) % 0.26/0.46 (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 @t75)))))))))))))))))))))))))) % 0.26/0.46 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t75))) % 0.26/0.46 (assume @p48 (= tptp.substmonoid (and @t27 @t24 @t30))) % 0.26/0.46 (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)))))))))))))))))))))))))))) % 0.26/0.46 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.26/0.46 (assume @p51 (= tptp.termmset (and @t22 @t15))) % 0.26/0.46 (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))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.26/0.46 (assume @p54 (= tptp.hoasapinj1 (forall @t43 (=> @t78 @t38)))) % 0.26/0.46 (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)))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.26/0.46 (assume @p57 (= tptp.hoasapinj2 (forall @t43 (=> @t78 @t44)))) % 0.26/0.46 (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))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.26/0.46 (assume @p60 (= tptp.hoaslaminj (forall @t92 (=> @t91 (forall (@list @t79) (=> (forall @t87 (= (_ (_ tptp.sub @t80) @t19) (_ (_ @t79 @t20) @t28))) (=> (= @t86 (_ @t85 (lambda @t84 @t80))) (forall @t84 (= @t83 @t80))))))))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.26/0.46 (assume @p63 @t100) % 0.26/0.46 (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))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p65 @t102) % 0.26/0.46 (assume @p66 (= tptp.hoaslamnotvar (forall @t92 (=> @t91 (not (_ (_ @t103 @t86) tptp.id)))))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.26/0.46 (assume @p69 (= tptp.hoasapnotvar (forall @t45 (not (_ (_ @t103 @t93) tptp.id))))) % 0.26/0.46 (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))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.26/0.46 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t106 (exists @t58 @t105)))) % 0.26/0.46 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.26/0.46 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t116 (=> @t115 (=> @t114 (=> @t110 (=> @t105 (forall @t14 (=> @t33 @t107))))))))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t116 (=> @t115 (=> @t114 (=> @t118 (=> @t105 (forall @t45 (=> @t107 (=> @t70 (_ @t56 @t9))))))))))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t66 (exists @t92 (forall @t12 (= @t83 @t68)))))) % 0.26/0.46 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.26/0.46 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t116 (=> @t115 (=> @t114 @t121))))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.26/0.46 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t116 @t121))) % 0.26/0.46 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.26/0.46 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t106 (=> @t115 (=> @t114 (=> @t110 (forall @t14 (=> @t33 @t109)))))))) % 0.26/0.46 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t122)) % 0.26/0.46 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t122)) % 0.26/0.46 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t106 (=> @t115 (=> @t114 (=> @t118 (forall @t45 (=> @t109 (=> @t117 (_ (_ @t108 @t9) tptp.id)))))))))) % 0.26/0.46 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t123)) % 0.26/0.46 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t123)) % 0.26/0.46 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t106 (=> @t120 @t125)))) % 0.26/0.46 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.26/0.46 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t106 (=> (forall @t92 (=> (exists @t64 (forall @t87 (and (= @t89 (_ (_ tptp.sub (_ @t63 @t10)) @t19)) (= (_ @t63 @t29) @t88)))) @t119)) @t125)))) % 0.26/0.46 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t106 (=> @t115 (=> @t114 @t126))))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.26/0.46 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t106 @t126))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.26/0.46 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t66 (exists @t92 (= (_ @t3 @t31) @t128))))) % 0.26/0.46 (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)))))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.26/0.46 (assume @p103 (= tptp.hoasinduction (forall @t106 (=> @t115 (=> @t114 (=> @t110 @t129)))))) % 0.26/0.46 (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 @t130)))))))))))))))))))))))))))))))))))) % 0.26/0.46 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t130))) % 0.26/0.46 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.26/0.46 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t106 @t129))) % 0.26/0.46 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.26/0.46 (assume @p109 @t131) % 0.26/0.46 (assume @p110 true) % 0.26/0.46 (step @p111 (= tptp.pushprop_p_and_p_prime @t135) :rule refl :args (@t135)) % 0.26/0.46 (step @p112 (= tptp.hoasap @t137) :rule refl :args (@t137)) % 0.26/0.46 (step @p113 (= tptp.hoaslam @t139) :rule refl :args (@t139)) % 0.26/0.46 (step @p114 (= tptp.hoasvar @t140) :rule refl :args (@t140)) % 0.26/0.46 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t141) :rule refl :args (@t141)) % 0.26/0.46 (step @p116 :rule quant-merge-prenex :args ((= (forall @t92 @t157) @t155))) % 0.26/0.46 (step @p117 :rule alpha_equiv :args (@t158 (@list @t143 @t142) (@list @t5 @t2))) % 0.26/0.46 (step @p118 :rule refl :args (@t153)) % 0.26/0.46 (step @p119 :rule nary_cong :premises (@p118 @p117) :args (@t159)) % 0.26/0.46 (step @p120 :rule quant-miniscope-or :args ((= @t157 @t159))) % 0.26/0.46 (step @p121 :rule trans :premises (@p120 @p119)) % 0.26/0.46 (step @p122 :rule symm :premises (@p121)) % 0.26/0.46 (step @p123 :rule cong :premises (@p122) :args ((forall @t92 (or @t153 @t162)))) % 0.26/0.46 (step @p124 :rule trans :premises (@p123 @p116)) % 0.26/0.46 (step @p125 :rule bool-impl-elim :args (@t152 @t162)) % 0.26/0.46 (step @p126 :rule cong :premises (@p125) :args ((forall @t92 (=> @t152 @t162)))) % 0.26/0.46 (step @p127 :rule trans :premises (@p126 @p124)) % 0.26/0.46 (step @p128 :rule refl :args ((tptp.ap @t13 @t2))) % 0.26/0.46 (step @p129 :rule refl :args (@t2)) % 0.26/0.46 (step @p130 :rule refl :args (@t160)) % 0.26/0.46 (step @p131 :rule cong :premises (@p130 @p129) :args (@t161)) % 0.26/0.46 (step @p132 :rule trans :premises (@p131 @p128)) % 0.26/0.46 (step @p133 :rule refl :args (tptp.ap)) % 0.26/0.46 (step @p134 :rule ho_cong :premises (@p133 @p130)) % 0.26/0.46 (step @p135 :rule ho_cong :premises (@p134 @p129)) % 0.26/0.46 (step @p136 :rule cong :premises (@p135 @p132) :args ((= (_ (_ tptp.ap @t160) @t2) @t161))) % 0.26/0.46 (step @p137 :rule symm :premises (@p136)) % 0.26/0.46 (step @p138 :rule refl :args (@t163)) % 0.26/0.46 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.26/0.46 (step @p140 :rule refl :args (@t13)) % 0.26/0.46 (step @p141 :rule cong :premises (@p140 @p130) :args ((= @t13 @t160))) % 0.26/0.46 (step @p142 :rule symm :premises (@p141)) % 0.26/0.46 (step @p143 :rule eq_resolve :premises (@p140 @p142)) % 0.26/0.46 (step @p144 :rule ho_cong :premises (@p133 @p143)) % 0.26/0.46 (step @p145 :rule ho_cong :premises (@p144 @p129)) % 0.26/0.46 (step @p146 :rule trans :premises (@p145 @p139)) % 0.26/0.46 (step @p147 :rule refl :args ((tptp.lam @t128))) % 0.26/0.46 (step @p148 :rule refl :args (@t144)) % 0.26/0.46 (step @p149 :rule cong :premises (@p148) :args (@t145)) % 0.26/0.46 (step @p150 :rule trans :premises (@p149 @p147)) % 0.26/0.46 (step @p151 :rule refl :args (tptp.lam)) % 0.26/0.46 (step @p152 :rule ho_cong :premises (@p151 @p148)) % 0.26/0.46 (step @p153 :rule cong :premises (@p152 @p150) :args ((= (_ tptp.lam @t144) @t145))) % 0.26/0.46 (step @p154 :rule symm :premises (@p153)) % 0.26/0.46 (step @p155 :rule refl :args (@t138)) % 0.26/0.46 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.26/0.46 (step @p157 :rule refl :args (@t128)) % 0.26/0.46 (step @p158 :rule cong :premises (@p157 @p148) :args ((= @t128 @t144))) % 0.26/0.46 (step @p159 :rule symm :premises (@p158)) % 0.26/0.46 (step @p160 :rule eq_resolve :premises (@p157 @p159)) % 0.26/0.46 (step @p161 :rule ho_cong :premises (@p151 @p160)) % 0.26/0.46 (step @p162 :rule trans :premises (@p161 @p156)) % 0.26/0.46 (step @p163 :rule cong :premises (@p162 @p146) :args (@t164)) % 0.26/0.46 (step @p164 :rule cong :premises (@p163) :args (@t165)) % 0.26/0.46 (step @p165 :rule cong :premises (@p164) :args ((forall @t45 @t165))) % 0.26/0.46 (step @p166 :rule beta-reduce :args ((= (_ @t166 @t2) @t163))) % 0.26/0.46 (step @p167 :rule refl :args (@t2)) % 0.26/0.46 (step @p168 :rule beta-reduce :args ((= (_ @t167 tptp.id) @t166))) % 0.26/0.46 (step @p169 :rule refl :args (tptp.id)) % 0.26/0.46 (step @p170 :rule beta-reduce :args ((= (_ @t168 @t5) @t167))) % 0.26/0.46 (step @p171 :rule refl :args (@t5)) % 0.26/0.46 (step @p172 :rule beta-reduce :args ((= @t169 @t168))) % 0.26/0.46 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 0.26/0.46 (step @p174 :rule trans :premises (@p173 @p170)) % 0.26/0.46 (step @p175 :rule ho_cong :premises (@p174 @p169)) % 0.26/0.46 (step @p176 :rule trans :premises (@p175 @p168)) % 0.26/0.46 (step @p177 :rule ho_cong :premises (@p176 @p167)) % 0.26/0.46 (step @p178 :rule trans :premises (@p177 @p166)) % 0.26/0.46 (step @p179 :rule beta-reduce :args ((= (_ @t170 tptp.one) @t128))) % 0.26/0.46 (step @p180 :rule refl :args (tptp.one)) % 0.26/0.46 (step @p181 :rule beta-reduce :args ((= @t171 @t170))) % 0.26/0.46 (step @p182 :rule ho_cong :premises (@p181 @p180)) % 0.26/0.46 (step @p183 :rule trans :premises (@p182 @p179)) % 0.26/0.46 (step @p184 :rule refl :args (tptp.lam)) % 0.26/0.46 (step @p185 :rule ho_cong :premises (@p184 @p183)) % 0.26/0.46 (step @p186 :rule beta-reduce :args ((= (_ @t172 @t94) (_ tptp.lam (_ @t171 tptp.one))))) % 0.26/0.46 (step @p187 :rule trans :premises (@p186 @p185)) % 0.26/0.46 (step @p188 :rule refl :args (@t94)) % 0.26/0.46 (step @p189 :rule beta-reduce :args ((= @t173 @t172))) % 0.26/0.46 (step @p190 :rule ho_cong :premises (@p189 @p188)) % 0.26/0.46 (step @p191 :rule trans :premises (@p190 @p187)) % 0.26/0.46 (step @p192 :rule cong :premises (@p191 @p178) :args (@t174)) % 0.26/0.46 (step @p193 :rule cong :premises (@p192) :args (@t175)) % 0.26/0.46 (step @p194 :rule cong :premises (@p193) :args (@t176)) % 0.26/0.46 (step @p195 :rule trans :premises (@p194 @p165)) % 0.26/0.46 (step @p196 :rule refl :args ((_ @t81 @t20 @t28))) % 0.26/0.46 (step @p197 :rule refl :args (@t147)) % 0.26/0.46 (step @p198 :rule refl :args (@t148)) % 0.26/0.46 (step @p199 :rule cong :premises (@p198 @p197) :args (@t149)) % 0.26/0.46 (step @p200 :rule trans :premises (@p199 @p196)) % 0.26/0.46 (step @p201 :rule refl :args (@t81)) % 0.26/0.46 (step @p202 :rule ho_cong :premises (@p201 @p198)) % 0.26/0.46 (step @p203 :rule ho_cong :premises (@p202 @p197)) % 0.26/0.46 (step @p204 :rule cong :premises (@p203 @p200) :args ((= (_ (_ @t81 @t148) @t147) @t149))) % 0.26/0.46 (step @p205 :rule symm :premises (@p204)) % 0.26/0.46 (step @p206 :rule refl :args (@t88)) % 0.26/0.46 (step @p207 :rule eq_resolve :premises (@p206 @p205)) % 0.26/0.46 (step @p208 :rule refl :args (@t28)) % 0.26/0.46 (step @p209 :rule cong :premises (@p208 @p197) :args ((= @t28 @t147))) % 0.26/0.46 (step @p210 :rule symm :premises (@p209)) % 0.26/0.46 (step @p211 :rule eq_resolve :premises (@p208 @p210)) % 0.26/0.46 (step @p212 :rule refl :args (@t20)) % 0.26/0.46 (step @p213 :rule cong :premises (@p212 @p198) :args ((= @t20 @t148))) % 0.26/0.46 (step @p214 :rule symm :premises (@p213)) % 0.26/0.46 (step @p215 :rule eq_resolve :premises (@p212 @p214)) % 0.26/0.46 (step @p216 :rule ho_cong :premises (@p201 @p215)) % 0.26/0.46 (step @p217 :rule ho_cong :premises (@p216 @p211)) % 0.26/0.46 (step @p218 :rule trans :premises (@p217 @p207)) % 0.26/0.46 (step @p219 :rule refl :args ((tptp.sub @t83 @t19))) % 0.26/0.46 (step @p220 :rule refl :args (@t19)) % 0.26/0.46 (step @p221 :rule refl :args (@t150)) % 0.26/0.46 (step @p222 :rule cong :premises (@p221 @p220) :args (@t151)) % 0.26/0.46 (step @p223 :rule trans :premises (@p222 @p219)) % 0.26/0.46 (step @p224 :rule refl :args (tptp.sub)) % 0.26/0.46 (step @p225 :rule ho_cong :premises (@p224 @p221)) % 0.26/0.46 (step @p226 :rule ho_cong :premises (@p225 @p220)) % 0.26/0.46 (step @p227 :rule cong :premises (@p226 @p223) :args ((= (_ (_ tptp.sub @t150) @t19) @t151))) % 0.26/0.46 (step @p228 :rule symm :premises (@p227)) % 0.26/0.46 (step @p229 :rule refl :args (@t89)) % 0.26/0.46 (step @p230 :rule eq_resolve :premises (@p229 @p228)) % 0.26/0.46 (step @p231 :rule refl :args (@t83)) % 0.26/0.46 (step @p232 :rule cong :premises (@p231 @p221) :args ((= @t83 @t150))) % 0.26/0.46 (step @p233 :rule symm :premises (@p232)) % 0.26/0.46 (step @p234 :rule eq_resolve :premises (@p231 @p233)) % 0.26/0.46 (step @p235 :rule ho_cong :premises (@p224 @p234)) % 0.26/0.46 (step @p236 :rule ho_cong :premises (@p235 @p220)) % 0.26/0.46 (step @p237 :rule trans :premises (@p236 @p230)) % 0.26/0.46 (step @p238 :rule cong :premises (@p237 @p218) :args (@t90)) % 0.26/0.46 (step @p239 :rule cong :premises (@p238) :args (@t91)) % 0.26/0.46 (step @p240 :rule cong :premises (@p239 @p195) :args (@t177)) % 0.26/0.46 (step @p241 :rule cong :premises (@p240) :args (@t178)) % 0.26/0.46 (step @p242 :rule trans :premises (@p241 @p127)) % 0.26/0.46 (step @p243 :rule refl :args (tptp.hoaslamnotap)) % 0.26/0.46 (step @p244 :rule cong :premises (@p243 @p242) :args ((= tptp.hoaslamnotap @t178))) % 0.26/0.46 (step @p245 :rule ho_cong :premises (@p112 @p169)) % 0.26/0.46 (step @p246 :rule ho_cong :premises (@p245 @p171)) % 0.26/0.46 (step @p247 :rule ho_cong :premises (@p246 @p169)) % 0.26/0.46 (step @p248 :rule ho_cong :premises (@p247 @p167)) % 0.26/0.46 (step @p249 :rule ho_cong :premises (@p113 @p169)) % 0.26/0.46 (step @p250 :rule ho_cong :premises (@p249 @p188)) % 0.26/0.46 (step @p251 :rule cong :premises (@p250 @p248) :args (@t95)) % 0.26/0.46 (step @p252 :rule cong :premises (@p251) :args (@t96)) % 0.26/0.46 (step @p253 :rule cong :premises (@p252) :args (@t97)) % 0.26/0.46 (step @p254 :rule refl :args (@t91)) % 0.26/0.46 (step @p255 :rule cong :premises (@p254 @p253) :args (@t98)) % 0.26/0.46 (step @p256 :rule cong :premises (@p255) :args (@t99)) % 0.26/0.46 (step @p257 :rule cong :premises (@p243 @p256) :args (@t100)) % 0.26/0.46 (step @p258 :rule trans :premises (@p257 @p244)) % 0.26/0.46 (step @p259 :rule eq_resolve :premises (@p63 @p258)) % 0.26/0.46 (step @p260 :rule refl :args (@t179)) % 0.26/0.46 (step @p261 :rule refl :args (@t46)) % 0.26/0.46 (step @p262 :rule cong :premises (@p261 @p260) :args ((= @t46 @t179))) % 0.26/0.46 (step @p263 :rule symm :premises (@p262)) % 0.26/0.46 (step @p264 :rule eq_resolve :premises (@p261 @p263)) % 0.26/0.46 (step @p265 :rule refl :args (@t180)) % 0.26/0.46 (step @p266 :rule refl :args (@t18)) % 0.26/0.46 (step @p267 :rule cong :premises (@p266 @p265) :args ((= @t18 @t180))) % 0.26/0.46 (step @p268 :rule symm :premises (@p267)) % 0.26/0.46 (step @p269 :rule eq_resolve :premises (@p266 @p268)) % 0.26/0.46 (step @p270 :rule cong :premises (@p269 @p264) :args (@t47)) % 0.26/0.46 (step @p271 :rule cong :premises (@p270) :args (@t48)) % 0.26/0.46 (step @p272 :rule cong :premises (@p271) :args (@t50)) % 0.26/0.46 (step @p273 :rule refl :args (tptp.lamnotap)) % 0.26/0.46 (step @p274 :rule cong :premises (@p273 @p272) :args (@t51)) % 0.26/0.46 (step @p275 :rule eq_resolve :premises (@p20 @p274)) % 0.26/0.46 (step @p276 :rule cong :premises (@p275 @p259) :args (@t101)) % 0.26/0.46 (step @p277 :rule refl :args (tptp.hoaslamnotap_lthm)) % 0.26/0.46 (step @p278 :rule cong :premises (@p277 @p276) :args (@t102)) % 0.26/0.46 (step @p279 :rule eq_resolve :premises (@p65 @p278)) % 0.26/0.46 (step @p280 :rule cong :premises (@p279) :args (@t131)) % 0.26/0.46 (step @p281 :rule eq_resolve :premises (@p109 @p280)) % 0.26/0.46 (step @p282 :rule not_implies_elim1 :premises (@p281)) % 0.26/0.46 (step @p283 :rule not_implies_elim2 :premises (@p281)) % 0.26/0.46 (step @p284 :rule skolemize :premises (@p283)) % 0.26/0.46 (step @p285 :rule bool-double-not-elim :args (@t185)) % 0.26/0.46 (step @p286 :rule refl :args (@t187)) % 0.26/0.46 (step @p287 :rule nary_cong :premises (@p286 @p285) :args ((or @t187 (not @t186)))) % 0.26/0.46 (step @p288 :rule cnf_or_neg :args (@t187 1)) % 0.26/0.46 (step @p289 :rule eq_resolve :premises (@p288 @p287)) % 0.26/0.46 (step @p290 :rule reordering :premises (@p289) :args ((or @t185 @t187))) % 0.26/0.46 (step @p291 :rule chain_m_resolution :premises (@p290 @p284) :args (@t185 (@list true) (@list @t187))) % 0.26/0.46 (assume-push @p298 @t188) % 0.26/0.46 (step @p293 :rule instantiate :premises (@p282) :args ((@list @t184 @t182 @t181))) % 0.26/0.46 (step-pop @p299 :rule scope :premises (@p293)) % 0.26/0.46 (step @p294 :rule process_scope :premises (@p299) :args (@t186)) % 0.26/0.46 (step @p296 :rule implies_elim :premises (@p294)) % 0.26/0.46 (step @p297 false :rule chain_m_resolution :premises (@p296 @p291 @p282) :args (false (@list false false) (@list @t185 @t188))) % 0.26/0.46 ) % 0.26/0.46 % SZS output end Proof % 0.26/0.46 % cvc5 exiting %------------------------------------------------------------------------------