%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG255^1 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:05:39 AM UTC 2026 % Result : Theorem 0.41s 0.70s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG255^1 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n002.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Wed Jun 3 01:55:03 EDT 2026 % 0.15/0.34 % CPUTime : % 0.36/0.56 %----Proving TH0 % 0.41/0.70 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.70 % SZS status Theorem % 0.41/0.70 % SZS output start Proof % 0.41/0.70 ( % 0.41/0.70 (declare-sort tptp.term 0) % 0.41/0.70 (declare-sort tptp.subst 0) % 0.41/0.70 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.41/0.70 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.41/0.70 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.41/0.70 (declare-const tptp.one tptp.term) % 0.41/0.70 (declare-const tptp.sh tptp.subst) % 0.41/0.70 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.41/0.70 (declare-const tptp.var (-> tptp.term Bool)) % 0.41/0.70 (declare-const tptp.id tptp.subst) % 0.41/0.70 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3b Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3a Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3 Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem2 Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem1 Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasinduction_lem0 Bool) % 0.41/0.70 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasapnotvar Bool) % 0.41/0.70 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.41/0.70 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.41/0.70 (declare-const tptp.hoaslamnotvar Bool) % 0.41/0.70 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.41/0.70 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.41/0.70 (declare-const tptp.hoaslamnotap Bool) % 0.41/0.70 (declare-const tptp.hoaslaminj_lthm Bool) % 0.41/0.70 (declare-const tptp.hoaslaminj_gthm Bool) % 0.41/0.70 (declare-const tptp.hoaslaminj Bool) % 0.41/0.70 (declare-const tptp.hoasapinj2_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasapinj2_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasapinj2 Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.41/0.70 (declare-const tptp.axassoc Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.41/0.70 (declare-const tptp.axvarcons Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem0 Bool) % 0.41/0.70 (declare-const tptp.apinj1 Bool) % 0.41/0.70 (declare-const tptp.induction Bool) % 0.41/0.70 (declare-const tptp.apnotvar Bool) % 0.41/0.70 (declare-const tptp.laminj Bool) % 0.41/0.70 (declare-const tptp.axvarshift Bool) % 0.41/0.70 (declare-const tptp.ulamvarind Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.41/0.70 (declare-const tptp.ulamvarsh Bool) % 0.41/0.70 (declare-const tptp.ulamvar1 Bool) % 0.41/0.70 (declare-const tptp.axabs Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem1 Bool) % 0.41/0.70 (declare-const tptp.shinj Bool) % 0.41/0.70 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.41/0.70 (declare-const tptp.apinj2 Bool) % 0.41/0.70 (declare-const tptp.axvarid Bool) % 0.41/0.70 (declare-const tptp.axidl Bool) % 0.41/0.70 (declare-const tptp.axclos Bool) % 0.41/0.70 (declare-const tptp.termmset Bool) % 0.41/0.70 (declare-const tptp.axshiftcons Bool) % 0.41/0.70 (declare-const tptp.lamnotap Bool) % 0.41/0.70 (declare-const tptp.lamnotvar Bool) % 0.41/0.70 (declare-const tptp.axapp Bool) % 0.41/0.70 (declare-const tptp.axscons Bool) % 0.41/0.70 (declare-const tptp.axmap Bool) % 0.41/0.70 (declare-const tptp.axidr Bool) % 0.41/0.70 (declare-const tptp.induction2lem Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasapinj1_lthm Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem1v2 Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.41/0.70 (declare-const tptp.induction2 Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem2v2 Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem3v2 Bool) % 0.41/0.70 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.41/0.70 (declare-const tptp.pushprop Bool) % 0.41/0.70 (declare-const tptp.pushprop_gthm Bool) % 0.41/0.70 (declare-const tptp.hoasapinj1 Bool) % 0.41/0.70 (declare-const tptp.pushprop_lthm_orig Bool) % 0.41/0.70 (declare-const tptp.pushprop_lthm Bool) % 0.41/0.70 (declare-const tptp.induction2lem_gthm Bool) % 0.41/0.70 (declare-const tptp.induction2lem_lthm Bool) % 0.41/0.70 (declare-const tptp.induction2_gthm Bool) % 0.41/0.70 (declare-const tptp.induction2_lthm Bool) % 0.41/0.70 (declare-const tptp.substmonoid Bool) % 0.41/0.70 (declare-const tptp.substmonoid_gthm Bool) % 0.41/0.70 (declare-const tptp.termmset_gthm Bool) % 0.41/0.70 (declare-const tptp.substmonoid_lthm Bool) % 0.41/0.70 (declare-const tptp.termmset_lthm Bool) % 0.41/0.70 (declare-const tptp.hoasapinj1_gthm Bool) % 0.41/0.70 (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)))))))))))) % 0.41/0.70 (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)))))) % 0.41/0.70 (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))))) % 0.41/0.70 (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)))))) % 0.41/0.70 (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)))))))) % 0.41/0.70 (define @t1 () (@var "M" tptp.subst)) % 0.41/0.70 (define @t2 () (@var "B" tptp.term)) % 0.41/0.70 (define @t3 () (_ tptp.sub @t2)) % 0.41/0.70 (define @t4 () (_ @t3 @t1)) % 0.41/0.70 (define @t5 () (@var "A" tptp.term)) % 0.41/0.70 (define @t6 () (_ tptp.sub @t5)) % 0.41/0.70 (define @t7 () (_ @t6 @t1)) % 0.41/0.70 (define @t8 () (_ tptp.ap @t5)) % 0.41/0.70 (define @t9 () (_ @t8 @t2)) % 0.41/0.70 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.41/0.70 (define @t11 () (_ tptp.sub tptp.one)) % 0.41/0.70 (define @t12 () (@list @t5 @t1)) % 0.41/0.70 (define @t13 () (_ @t6 tptp.id)) % 0.41/0.70 (define @t14 () (@list @t5)) % 0.41/0.70 (define @t15 () (forall @t14 (= @t13 @t5))) % 0.41/0.70 (define @t16 () (= tptp.axvarid @t15)) % 0.41/0.70 (define @t17 () (_ tptp.comp @t1)) % 0.41/0.70 (define @t18 () (_ tptp.push tptp.one)) % 0.41/0.70 (define @t19 () (_ tptp.lam @t5)) % 0.41/0.70 (define @t20 () (@var "N" tptp.subst)) % 0.41/0.70 (define @t21 () (_ @t17 @t20)) % 0.41/0.70 (define @t22 () (_ @t6 @t21)) % 0.41/0.70 (define @t23 () (_ (_ tptp.sub @t7) @t20)) % 0.41/0.70 (define @t24 () (= @t23 @t22)) % 0.41/0.70 (define @t25 () (@list @t5 @t1 @t20)) % 0.41/0.70 (define @t26 () (forall @t25 @t24)) % 0.41/0.70 (define @t27 () (= tptp.axclos @t26)) % 0.41/0.70 (define @t28 () (@list @t1)) % 0.41/0.70 (define @t29 () (forall @t28 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 0.41/0.70 (define @t30 () (_ tptp.comp tptp.sh)) % 0.41/0.70 (define @t31 () (@var "K" tptp.subst)) % 0.41/0.70 (define @t32 () (forall (@list @t1 @t20 @t31) (= (_ (_ tptp.comp @t21) @t31) (_ @t17 (_ (_ tptp.comp @t20) @t31))))) % 0.41/0.70 (define @t33 () (_ @t6 @t20)) % 0.41/0.70 (define @t34 () (_ (_ tptp.push @t33) @t21)) % 0.41/0.70 (define @t35 () (forall @t28 (= (_ @t17 tptp.id) @t1))) % 0.41/0.70 (define @t36 () (_ @t18 tptp.sh)) % 0.41/0.70 (define @t37 () (_ @t6 tptp.sh)) % 0.41/0.70 (define @t38 () (_ tptp.var @t5)) % 0.41/0.70 (define @t39 () (@var "P" (-> tptp.term Bool))) % 0.41/0.70 (define @t40 () (_ @t39 @t5)) % 0.41/0.70 (define @t41 () (forall @t14 (=> @t38 @t40))) % 0.41/0.70 (define @t42 () (@list @t39)) % 0.41/0.70 (define @t43 () (= @t5 @t2)) % 0.41/0.70 (define @t44 () (@var "D" tptp.term)) % 0.41/0.70 (define @t45 () (_ tptp.ap @t2)) % 0.41/0.70 (define @t46 () (@var "C" tptp.term)) % 0.41/0.70 (define @t47 () (= (_ @t8 @t46) (_ @t45 @t44))) % 0.41/0.70 (define @t48 () (@list @t5 @t2 @t46 @t44)) % 0.41/0.70 (define @t49 () (= @t46 @t44)) % 0.41/0.70 (define @t50 () (@list @t5 @t2)) % 0.41/0.70 (define @t51 () (forall @t14 @t40)) % 0.41/0.70 (define @t52 () (_ @t39 @t19)) % 0.41/0.70 (define @t53 () (_ @t39 @t2)) % 0.41/0.70 (define @t54 () (forall @t50 (=> @t40 (=> @t53 (_ @t39 @t9))))) % 0.41/0.70 (define @t55 () (@var "Q" (-> tptp.term Bool))) % 0.41/0.70 (define @t56 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t39) @t55)) % 0.41/0.70 (define @t57 () (@list @t55)) % 0.41/0.70 (define @t58 () (@list @t39 @t5 @t1)) % 0.41/0.70 (define @t59 () (_ tptp.push @t2)) % 0.41/0.70 (define @t60 () (@var "K" (-> tptp.term Bool))) % 0.41/0.70 (define @t61 () (@list @t39 @t55 @t5 @t1)) % 0.41/0.70 (define @t62 () (_ tptp.sub @t46)) % 0.41/0.70 (define @t63 () (@list @t46)) % 0.41/0.70 (define @t64 () (_ tptp.var @t2)) % 0.41/0.70 (define @t65 () (@list @t2)) % 0.41/0.70 (define @t66 () (forall @t65 (=> @t64 (_ @t39 @t4)))) % 0.41/0.70 (define @t67 () (_ @t3 @t10)) % 0.41/0.70 (define @t68 () (forall @t65 (=> @t64 (_ @t39 @t67)))) % 0.41/0.70 (define @t69 () (_ @t55 @t2)) % 0.41/0.70 (define @t70 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.41/0.70 (define @t71 () (_ @t6 (_ @t59 tptp.id))) % 0.41/0.70 (define @t72 () (forall @t14 (=> (forall @t65 (=> @t53 (_ @t39 @t71))) @t52))) % 0.41/0.70 (define @t73 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.41/0.70 (define @t74 () (=> tptp.induction2lem tptp.induction2)) % 0.41/0.70 (define @t75 () (and @t26 @t15)) % 0.41/0.70 (define @t76 () (= tptp.termmset @t75)) % 0.41/0.70 (define @t77 () (=> tptp.substmonoid tptp.termmset)) % 0.41/0.70 (define @t78 () (_ tptp.hoasap tptp.id)) % 0.41/0.70 (define @t79 () (_ (_ @t78 @t5) tptp.id)) % 0.41/0.70 (define @t80 () (= (_ @t79 @t46) (_ (_ (_ @t78 @t2) tptp.id) @t44))) % 0.41/0.70 (define @t81 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.70 (define @t82 () (_ (_ @t81 @t1) @t5)) % 0.41/0.70 (define @t83 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.70 (define @t84 () (_ @t83 @t1)) % 0.41/0.70 (define @t85 () (_ @t84 @t5)) % 0.41/0.70 (define @t86 () (@list @t1 @t5)) % 0.41/0.70 (define @t87 () (_ tptp.hoaslam tptp.id)) % 0.41/0.70 (define @t88 () (_ @t87 (lambda @t86 @t85))) % 0.41/0.70 (define @t89 () (@list @t1 @t5 @t20)) % 0.41/0.70 (define @t90 () (_ (_ @t83 @t21) @t33)) % 0.41/0.70 (define @t91 () (_ (_ tptp.sub @t85) @t20)) % 0.41/0.70 (define @t92 () (forall @t89 (= @t91 @t90))) % 0.41/0.70 (define @t93 () (@list @t83)) % 0.41/0.70 (define @t94 () (_ @t79 @t2)) % 0.41/0.70 (define @t95 () (_ tptp.hoasvar tptp.id)) % 0.41/0.70 (define @t96 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.41/0.70 (define @t97 () (_ (_ tptp.hoasinduction_p_and_p_prime @t96) @t55)) % 0.41/0.70 (define @t98 () (@list @t96)) % 0.41/0.70 (define @t99 () (_ @t55 @t5)) % 0.41/0.70 (define @t100 () (_ @t96 tptp.id)) % 0.41/0.70 (define @t101 () (_ (_ @t100 @t5) tptp.id)) % 0.41/0.70 (define @t102 () (forall @t14 (=> (_ (_ @t95 @t5) tptp.id) @t101))) % 0.41/0.70 (define @t103 () (_ (_ (_ @t96 @t1) @t5) (_ (_ tptp.comp @t31) @t20))) % 0.41/0.70 (define @t104 () (_ (_ (_ @t96 (_ @t17 @t31)) (_ @t6 @t31)) @t20)) % 0.41/0.70 (define @t105 () (@list @t1 @t5 @t20 @t31)) % 0.41/0.70 (define @t106 () (forall @t105 (=> @t104 @t103))) % 0.41/0.70 (define @t107 () (forall @t105 (=> @t103 @t104))) % 0.41/0.70 (define @t108 () (@list @t96 @t55)) % 0.41/0.70 (define @t109 () (_ (_ @t100 @t2) tptp.id)) % 0.41/0.70 (define @t110 () (forall @t50 (=> @t101 (=> @t109 (_ (_ @t100 @t94) tptp.id))))) % 0.41/0.70 (define @t111 () (=> (forall @t14 (=> @t101 (_ (_ @t100 (_ (_ @t83 tptp.id) @t5)) tptp.id))) (_ (_ @t100 @t88) tptp.id))) % 0.41/0.70 (define @t112 () (forall @t93 (=> @t92 @t111))) % 0.41/0.70 (define @t113 () (=> @t112 (=> @t97 (forall @t14 (=> (forall @t65 (=> @t69 (_ @t55 @t71))) (_ @t55 @t19)))))) % 0.41/0.70 (define @t114 () (=> 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))))))))))))))))))))))))))))))))))) % 0.41/0.70 (define @t115 () (=> 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))))))))))))))))))))))))))))))))))) % 0.41/0.70 (define @t116 () (forall @t65 (=> @t109 (_ (_ @t100 @t71) tptp.id)))) % 0.41/0.70 (define @t117 () (forall @t14 (=> @t116 (_ (_ @t100 (_ tptp.lam (_ @t6 @t36))) tptp.id)))) % 0.41/0.70 (define @t118 () (=> @t112 (forall @t14 (=> @t116 (_ (_ @t100 @t19) tptp.id))))) % 0.41/0.70 (define @t119 () (_ (_ @t83 tptp.sh) tptp.one)) % 0.41/0.70 (define @t120 () (=> @t110 (=> @t112 (forall @t14 @t101)))) % 0.41/0.70 (define @t121 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.41/0.70 (define @t122 () (@var "X" tptp.term)) % 0.41/0.70 (define @t123 () (_ @t55 @t122)) % 0.41/0.70 (define @t124 () (@list @t122)) % 0.41/0.70 (define @t125 () (lambda (@list @t5 @t1 @t39 @t55) (forall @t124 (= @t123 (_ @t39 (_ (_ tptp.sub @t122) @t10)))))) % 0.41/0.70 (define @t126 () (lambda (@list @t1 @t5 @t20 @t2) (_ (_ tptp.ap @t33) @t2))) % 0.41/0.70 (define @t127 () (lambda (@list @t1 @t83) (_ tptp.lam @t119))) % 0.41/0.70 (define @t128 () (lambda @t89 (_ tptp.var @t33))) % 0.41/0.70 (define @t129 () (lambda @t108 (forall @t124 (= @t123 (_ (_ @t100 @t122) tptp.id))))) % 0.41/0.70 (define @t130 () (tptp.sub @t5 tptp.id)) % 0.41/0.70 (define @t131 () (= @t5 @t13)) % 0.41/0.70 (define @t132 () (tptp.comp @t1 @t20)) % 0.41/0.70 (define @t133 () (tptp.sub @t5 @t132)) % 0.41/0.70 (define @t134 () (tptp.sub @t5 @t1)) % 0.41/0.70 (define @t135 () (tptp.sub @t134 @t20)) % 0.41/0.70 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.41/0.70 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.41/0.70 (assume @p3 @t16) % 0.41/0.70 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t19) @t1) (_ tptp.lam (_ @t6 (_ @t18 (_ @t17 tptp.sh)))))))) % 0.41/0.70 (assume @p5 @t27) % 0.41/0.70 (assume @p6 (= tptp.axidl @t29)) % 0.41/0.70 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t30 @t10) @t1)))) % 0.41/0.70 (assume @p8 (= tptp.axassoc @t32)) % 0.41/0.70 (assume @p9 (= tptp.axmap (forall @t25 (= (_ (_ tptp.comp @t10) @t20) @t34)))) % 0.41/0.70 (assume @p10 (= tptp.axidr @t35)) % 0.41/0.70 (assume @p11 (= tptp.axvarshift (= @t36 tptp.id))) % 0.41/0.70 (assume @p12 (= tptp.axscons (forall @t28 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t30 @t1)) @t1)))) % 0.41/0.70 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.41/0.70 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t38 (_ tptp.var @t37))))) % 0.41/0.70 (assume @p15 (= tptp.ulamvarind (forall @t42 (=> (_ @t39 tptp.one) (=> (forall @t14 (=> @t38 (=> @t40 (_ @t39 @t37)))) @t41))))) % 0.41/0.70 (assume @p16 (= tptp.apinj1 (forall @t48 (=> @t47 @t43)))) % 0.41/0.70 (assume @p17 (= tptp.apinj2 (forall @t48 (=> @t47 @t49)))) % 0.41/0.70 (assume @p18 (= tptp.laminj (forall @t50 (=> (= @t19 (_ tptp.lam @t2)) @t43)))) % 0.41/0.70 (assume @p19 (= tptp.shinj (forall @t50 (=> (= @t37 (_ @t3 tptp.sh)) @t43)))) % 0.41/0.70 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t46) (not (= @t19 (_ @t45 @t46)))))) % 0.41/0.70 (assume @p21 (= tptp.apnotvar (forall @t50 (not (_ tptp.var @t9))))) % 0.41/0.70 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t19))))) % 0.41/0.70 (assume @p23 (= tptp.induction (forall @t42 (=> @t41 (=> @t54 (=> (forall @t14 (=> @t40 @t52)) @t51)))))) % 0.41/0.70 (assume @p24 (= tptp.pushprop_lem0 (forall @t58 (exists @t57 @t56)))) % 0.41/0.70 (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))))))))))))))))))))))))) % 0.41/0.70 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.41/0.70 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t39 @t60 @t5 @t1 @t2) (=> @t40 (_ @t60 (_ @t6 (_ @t59 @t1))))))) % 0.41/0.70 (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))))))))))))))))))))))))) % 0.41/0.70 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.41/0.70 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t61 (=> @t40 (=> @t56 (_ @t55 tptp.one)))))) % 0.41/0.70 (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))))))))))))))))))))))))) % 0.41/0.70 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.41/0.70 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t61 (=> @t56 (=> @t66 (forall @t63 (=> (_ tptp.var @t46) (=> (_ @t55 @t46) (_ @t55 (_ @t62 tptp.sh)))))))))) % 0.41/0.70 (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))))))))))))))))))))))))) % 0.41/0.70 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.41/0.70 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t61 (=> @t56 (=> (forall @t65 (=> @t64 @t69)) @t68))))) % 0.41/0.70 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.41/0.70 (assume @p38 (= tptp.pushprop (forall @t58 (=> @t66 (=> @t40 @t68))))) % 0.41/0.70 (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))))))))))))))))))))))))) % 0.41/0.70 (assume @p40 (= tptp.pushprop_lthm_orig @t70)) % 0.41/0.70 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t70))) % 0.41/0.70 (assume @p42 (= tptp.induction2lem (forall @t42 (=> @t54 (=> @t72 (forall @t12 (=> @t66 (_ @t39 @t7)))))))) % 0.41/0.70 (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 @t73)))))))))))))))))))))))) % 0.41/0.70 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t73)))))))))) % 0.41/0.70 (assume @p45 (= tptp.induction2 (forall @t42 (=> @t41 (=> @t54 (=> @t72 @t51)))))) % 0.41/0.70 (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 @t74)))))))))))))))))))))))))) % 0.41/0.70 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t74))) % 0.41/0.70 (assume @p48 (= tptp.substmonoid (and @t32 @t29 @t35))) % 0.41/0.70 (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)))))))))))))))))))))))))))) % 0.41/0.70 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.41/0.70 (assume @p51 @t76) % 0.41/0.70 (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 @t77)))))))))))))))))))))))))))) % 0.41/0.70 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.41/0.70 (assume @p54 (= tptp.hoasapinj1 (forall @t48 (=> @t80 @t43)))) % 0.41/0.70 (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)))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.41/0.70 (assume @p57 (= tptp.hoasapinj2 (forall @t48 (=> @t80 @t49)))) % 0.41/0.70 (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))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.41/0.70 (assume @p60 (= tptp.hoaslaminj (forall @t93 (=> @t92 (forall (@list @t81) (=> (forall @t89 (= (_ (_ tptp.sub @t82) @t20) (_ (_ @t81 @t21) @t33))) (=> (= @t88 (_ @t87 (lambda @t86 @t82))) (forall @t86 (= @t85 @t82))))))))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.41/0.70 (assume @p63 (= tptp.hoaslamnotap (forall @t93 (=> @t92 (forall @t50 (not (= (_ @t87 (lambda (@list @t1 @t46) (_ @t84 @t46))) @t94))))))) % 0.41/0.70 (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))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.41/0.70 (assume @p66 (= tptp.hoaslamnotvar (forall @t93 (=> @t92 (not (_ (_ @t95 @t88) tptp.id)))))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.41/0.70 (assume @p69 (= tptp.hoasapnotvar (forall @t50 (not (_ (_ @t95 @t94) tptp.id))))) % 0.41/0.70 (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))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.41/0.70 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t98 (exists @t57 @t97)))) % 0.41/0.70 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.41/0.70 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t108 (=> @t107 (=> @t106 (=> @t102 (=> @t97 (forall @t14 (=> @t38 @t99))))))))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t108 (=> @t107 (=> @t106 (=> @t110 (=> @t97 (forall @t50 (=> @t99 (=> @t69 (_ @t55 @t9))))))))))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t65 (exists @t93 (forall @t12 (= @t85 @t67)))))) % 0.41/0.70 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.41/0.70 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t108 (=> @t107 (=> @t106 @t113))))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.41/0.70 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t108 @t113))) % 0.41/0.70 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.41/0.70 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t98 (=> @t107 (=> @t106 (=> @t102 (forall @t14 (=> @t38 @t101)))))))) % 0.41/0.70 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t114)) % 0.41/0.70 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t114)) % 0.41/0.70 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t98 (=> @t107 (=> @t106 (=> @t110 (forall @t50 (=> @t101 (=> @t109 (_ (_ @t100 @t9) tptp.id)))))))))) % 0.41/0.70 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t115)) % 0.41/0.70 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t115)) % 0.41/0.70 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t98 (=> @t112 @t117)))) % 0.41/0.70 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.41/0.70 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t98 (=> (forall @t93 (=> (exists @t63 (forall @t89 (and (= @t91 (_ (_ tptp.sub (_ @t62 @t10)) @t20)) (= (_ @t62 @t34) @t90)))) @t111)) @t117)))) % 0.41/0.70 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t98 (=> @t107 (=> @t106 @t118))))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.41/0.70 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t98 @t118))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.41/0.70 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t65 (exists @t93 (= (_ @t3 @t36) @t119))))) % 0.41/0.70 (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)))))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.41/0.70 (assume @p103 (= tptp.hoasinduction (forall @t98 (=> @t107 (=> @t106 (=> @t102 @t120)))))) % 0.41/0.70 (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 @t121)))))))))))))))))))))))))))))))))))) % 0.41/0.70 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t121))) % 0.41/0.70 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.41/0.70 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t98 @t120))) % 0.41/0.70 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.41/0.70 (assume @p109 (not tptp.termmset_gthm)) % 0.41/0.70 (assume @p110 true) % 0.41/0.70 (step @p111 (= tptp.pushprop_p_and_p_prime @t125) :rule refl :args (@t125)) % 0.41/0.70 (step @p112 (= tptp.hoasap @t126) :rule refl :args (@t126)) % 0.41/0.70 (step @p113 (= tptp.hoaslam @t127) :rule refl :args (@t127)) % 0.41/0.70 (step @p114 (= tptp.hoasvar @t128) :rule refl :args (@t128)) % 0.41/0.70 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t129) :rule refl :args (@t129)) % 0.41/0.70 (step @p116 :rule equiv_elim2 :premises (@p52)) % 0.41/0.70 (step @p117 :rule resolution :premises (@p116 @p109) :args (true tptp.termmset_gthm)) % 0.41/0.70 (step @p118 :rule not_implies_elim2 :premises (@p117)) % 0.41/0.70 (step @p119 :rule not_implies_elim2 :premises (@p118)) % 0.41/0.70 (step @p120 :rule not_implies_elim2 :premises (@p119)) % 0.41/0.70 (step @p121 :rule not_implies_elim2 :premises (@p120)) % 0.41/0.70 (step @p122 :rule not_implies_elim2 :premises (@p121)) % 0.41/0.70 (step @p123 :rule not_implies_elim2 :premises (@p122)) % 0.41/0.70 (step @p124 :rule not_implies_elim2 :premises (@p123)) % 0.41/0.70 (step @p125 :rule not_implies_elim2 :premises (@p124)) % 0.41/0.70 (step @p126 :rule not_implies_elim2 :premises (@p125)) % 0.41/0.70 (step @p127 :rule not_implies_elim2 :premises (@p126)) % 0.41/0.70 (step @p128 :rule not_implies_elim2 :premises (@p127)) % 0.41/0.70 (step @p129 :rule not_implies_elim2 :premises (@p128)) % 0.41/0.70 (step @p130 :rule not_implies_elim2 :premises (@p129)) % 0.41/0.70 (step @p131 :rule not_implies_elim2 :premises (@p130)) % 0.41/0.70 (step @p132 :rule not_implies_elim2 :premises (@p131)) % 0.41/0.70 (step @p133 :rule not_implies_elim2 :premises (@p132)) % 0.41/0.70 (step @p134 :rule not_implies_elim2 :premises (@p133)) % 0.41/0.70 (step @p135 :rule not_implies_elim2 :premises (@p134)) % 0.41/0.70 (step @p136 :rule not_implies_elim2 :premises (@p135)) % 0.41/0.70 (step @p137 :rule not_implies_elim2 :premises (@p136)) % 0.41/0.70 (step @p138 :rule not_implies_elim2 :premises (@p137)) % 0.41/0.70 (step @p139 :rule not_implies_elim2 :premises (@p138)) % 0.41/0.70 (step @p140 :rule not_implies_elim2 :premises (@p139)) % 0.41/0.70 (step @p141 :rule not_implies_elim2 :premises (@p140)) % 0.41/0.70 (step @p142 :rule not_implies_elim2 :premises (@p141)) % 0.41/0.70 (step @p143 :rule not_implies_elim2 :premises (@p142)) % 0.41/0.70 (step @p144 :rule refl :args (@t130)) % 0.41/0.70 (step @p145 :rule refl :args (@t13)) % 0.41/0.70 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t13 @t130))) % 0.41/0.70 (step @p147 :rule symm :premises (@p146)) % 0.41/0.70 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.41/0.70 (step @p149 :rule refl :args (@t5)) % 0.41/0.70 (step @p150 :rule cong :premises (@p149 @p148) :args (@t131)) % 0.41/0.70 (step @p151 :rule cong :premises (@p150) :args ((forall @t14 @t131))) % 0.41/0.70 (step @p152 :rule eq-symm :args (@t13 @t5)) % 0.41/0.70 (step @p153 :rule cong :premises (@p152) :args (@t15)) % 0.41/0.70 (step @p154 :rule trans :premises (@p153 @p151)) % 0.41/0.70 (step @p155 :rule refl :args ((tptp.sub @t5 @t21))) % 0.41/0.70 (step @p156 :rule refl :args (@t132)) % 0.41/0.70 (step @p157 :rule cong :premises (@p149 @p156) :args (@t133)) % 0.41/0.70 (step @p158 :rule trans :premises (@p157 @p155)) % 0.41/0.70 (step @p159 :rule refl :args (@t6)) % 0.41/0.70 (step @p160 :rule ho_cong :premises (@p159 @p156)) % 0.41/0.70 (step @p161 :rule cong :premises (@p160 @p158) :args ((= (_ @t6 @t132) @t133))) % 0.41/0.70 (step @p162 :rule symm :premises (@p161)) % 0.41/0.70 (step @p163 :rule refl :args (@t22)) % 0.41/0.70 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.41/0.70 (step @p165 :rule refl :args (@t21)) % 0.41/0.70 (step @p166 :rule cong :premises (@p165 @p156) :args ((= @t21 @t132))) % 0.41/0.70 (step @p167 :rule symm :premises (@p166)) % 0.41/0.70 (step @p168 :rule eq_resolve :premises (@p165 @p167)) % 0.41/0.70 (step @p169 :rule ho_cong :premises (@p159 @p168)) % 0.41/0.70 (step @p170 :rule trans :premises (@p169 @p164)) % 0.41/0.70 (step @p171 :rule refl :args ((tptp.sub @t7 @t20))) % 0.41/0.70 (step @p172 :rule refl :args (@t20)) % 0.41/0.70 (step @p173 :rule refl :args (@t134)) % 0.41/0.70 (step @p174 :rule cong :premises (@p173 @p172) :args (@t135)) % 0.41/0.70 (step @p175 :rule trans :premises (@p174 @p171)) % 0.41/0.70 (step @p176 :rule refl :args (tptp.sub)) % 0.41/0.70 (step @p177 :rule ho_cong :premises (@p176 @p173)) % 0.41/0.70 (step @p178 :rule ho_cong :premises (@p177 @p172)) % 0.41/0.70 (step @p179 :rule cong :premises (@p178 @p175) :args ((= (_ (_ tptp.sub @t134) @t20) @t135))) % 0.41/0.70 (step @p180 :rule symm :premises (@p179)) % 0.41/0.70 (step @p181 :rule refl :args (@t23)) % 0.41/0.70 (step @p182 :rule eq_resolve :premises (@p181 @p180)) % 0.41/0.70 (step @p183 :rule refl :args (@t7)) % 0.41/0.70 (step @p184 :rule cong :premises (@p183 @p173) :args ((= @t7 @t134))) % 0.41/0.70 (step @p185 :rule symm :premises (@p184)) % 0.41/0.70 (step @p186 :rule eq_resolve :premises (@p183 @p185)) % 0.41/0.70 (step @p187 :rule ho_cong :premises (@p176 @p186)) % 0.41/0.70 (step @p188 :rule ho_cong :premises (@p187 @p172)) % 0.41/0.70 (step @p189 :rule trans :premises (@p188 @p182)) % 0.41/0.70 (step @p190 :rule cong :premises (@p189 @p170) :args (@t24)) % 0.41/0.70 (step @p191 :rule cong :premises (@p190) :args (@t26)) % 0.41/0.70 (step @p192 :rule nary_cong :premises (@p191 @p154) :args (@t75)) % 0.41/0.70 (step @p193 :rule refl :args (tptp.termmset)) % 0.41/0.70 (step @p194 :rule cong :premises (@p193 @p192) :args (@t76)) % 0.41/0.70 (step @p195 :rule eq_resolve :premises (@p51 @p194)) % 0.41/0.70 (step @p196 :rule symm :premises (@p195)) % 0.41/0.70 (step @p197 :rule refl :args (tptp.axvarid)) % 0.41/0.70 (step @p198 :rule cong :premises (@p197 @p154) :args (@t16)) % 0.41/0.70 (step @p199 :rule eq_resolve :premises (@p3 @p198)) % 0.41/0.70 (step @p200 :rule not_implies_elim1 :premises (@p119)) % 0.41/0.70 (step @p201 :rule eq_resolve :premises (@p200 @p199)) % 0.41/0.70 (step @p202 :rule refl :args (tptp.axclos)) % 0.41/0.70 (step @p203 :rule cong :premises (@p202 @p191) :args (@t27)) % 0.41/0.70 (step @p204 :rule eq_resolve :premises (@p5 @p203)) % 0.41/0.70 (step @p205 :rule not_implies_elim1 :premises (@p121)) % 0.41/0.70 (step @p206 :rule eq_resolve :premises (@p205 @p204)) % 0.41/0.70 (step @p207 :rule and_intro :premises (@p206 @p201)) % 0.41/0.70 (step @p208 :rule eq_resolve :premises (@p207 @p196)) % 0.41/0.70 (step @p209 :rule cnf_implies_neg2 :args (@t77)) % 0.41/0.70 (step @p210 :rule resolution :premises (@p209 @p208) :args (false tptp.termmset)) % 0.41/0.70 (step @p211 false :rule contra :premises (@p210 @p143)) % 0.41/0.70 ) % 0.41/0.70 % SZS output end Proof % 0.41/0.70 % cvc5 exiting %------------------------------------------------------------------------------