%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG267^2 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : 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 08:05:42 AM UTC 2026 % Result : Theorem 0.39s 0.76s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG267^2 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 01:55:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.39/0.55 %----Proving TH0 % 0.39/0.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.76 % SZS status Theorem % 0.39/0.76 % SZS output start Proof % 0.39/0.76 ( % 0.39/0.76 (declare-sort tptp.term 0) % 0.39/0.76 (declare-sort tptp.subst 0) % 0.39/0.76 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.39/0.76 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.39/0.76 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.39/0.76 (declare-const tptp.one tptp.term) % 0.39/0.76 (declare-const tptp.sh tptp.subst) % 0.39/0.76 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.39/0.76 (declare-const tptp.var (-> tptp.term Bool)) % 0.39/0.76 (declare-const tptp.id tptp.subst) % 0.39/0.76 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3b Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3a Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3 Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem2 Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem1 Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasinduction_lem0 Bool) % 0.39/0.76 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasapnotvar Bool) % 0.39/0.76 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.39/0.76 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.39/0.76 (declare-const tptp.hoaslamnotvar Bool) % 0.39/0.76 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.39/0.76 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.39/0.76 (declare-const tptp.hoaslamnotap Bool) % 0.39/0.76 (declare-const tptp.hoaslaminj_lthm Bool) % 0.39/0.76 (declare-const tptp.hoaslaminj_gthm Bool) % 0.39/0.76 (declare-const tptp.hoaslaminj Bool) % 0.39/0.76 (declare-const tptp.hoasapinj2_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasapinj2_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasapinj2 Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.39/0.76 (declare-const tptp.axassoc Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.39/0.76 (declare-const tptp.axvarcons Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem0 Bool) % 0.39/0.76 (declare-const tptp.apinj1 Bool) % 0.39/0.76 (declare-const tptp.induction Bool) % 0.39/0.76 (declare-const tptp.apnotvar Bool) % 0.39/0.76 (declare-const tptp.laminj Bool) % 0.39/0.76 (declare-const tptp.axvarshift Bool) % 0.39/0.76 (declare-const tptp.ulamvarind Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.39/0.76 (declare-const tptp.ulamvarsh Bool) % 0.39/0.76 (declare-const tptp.ulamvar1 Bool) % 0.39/0.76 (declare-const tptp.axabs Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem1 Bool) % 0.39/0.76 (declare-const tptp.shinj Bool) % 0.39/0.76 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.39/0.76 (declare-const tptp.apinj2 Bool) % 0.39/0.76 (declare-const tptp.axvarid Bool) % 0.39/0.76 (declare-const tptp.axidl Bool) % 0.39/0.76 (declare-const tptp.axclos Bool) % 0.39/0.76 (declare-const tptp.termmset Bool) % 0.39/0.76 (declare-const tptp.axshiftcons Bool) % 0.39/0.76 (declare-const tptp.lamnotap Bool) % 0.39/0.76 (declare-const tptp.lamnotvar Bool) % 0.39/0.76 (declare-const tptp.axapp Bool) % 0.39/0.76 (declare-const tptp.axscons Bool) % 0.39/0.76 (declare-const tptp.axmap Bool) % 0.39/0.76 (declare-const tptp.axidr Bool) % 0.39/0.76 (declare-const tptp.induction2lem Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasapinj1_lthm Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem1v2 Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.39/0.76 (declare-const tptp.induction2 Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem2v2 Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem3v2 Bool) % 0.39/0.76 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.39/0.76 (declare-const tptp.pushprop Bool) % 0.39/0.76 (declare-const tptp.pushprop_gthm Bool) % 0.39/0.76 (declare-const tptp.hoasapinj1 Bool) % 0.39/0.76 (declare-const tptp.pushprop_lthm_orig Bool) % 0.39/0.76 (declare-const tptp.pushprop_lthm Bool) % 0.39/0.76 (declare-const tptp.induction2lem_gthm Bool) % 0.39/0.76 (declare-const tptp.induction2lem_lthm Bool) % 0.39/0.76 (declare-const tptp.induction2_gthm Bool) % 0.39/0.76 (declare-const tptp.induction2_lthm Bool) % 0.39/0.76 (declare-const tptp.substmonoid Bool) % 0.39/0.76 (declare-const tptp.substmonoid_gthm Bool) % 0.39/0.76 (declare-const tptp.termmset_gthm Bool) % 0.39/0.76 (declare-const tptp.substmonoid_lthm Bool) % 0.39/0.76 (declare-const tptp.termmset_lthm Bool) % 0.39/0.76 (declare-const tptp.hoasapinj1_gthm Bool) % 0.39/0.76 (define tptp.pushprop_p_and_p_prime () (let ((_let_1 (@var "M" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (let ((_let_3 (@var "X" tptp.term))) (let ((_let_4 (@var "P" (-> tptp.term Bool)))) (let ((_let_5 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_1 _let_4 _let_5) (forall (@list _let_3) (= (_ _let_5 _let_3) (_ _let_4 (_ (_ tptp.sub _let_3) (_ (_ tptp.push _let_2) _let_1)))))))))))) % 0.39/0.76 (define tptp.hoasap () (let ((_let_1 (@var "B" tptp.term))) (let ((_let_2 (@var "N" tptp.subst))) (let ((_let_3 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_3 _let_2 _let_1) (_ (_ tptp.ap (_ (_ tptp.sub _let_3) _let_2)) _let_1)))))) % 0.39/0.76 (define tptp.hoaslam () (let ((_let_1 (@var "F" (-> tptp.subst tptp.term tptp.term)))) (lambda (@list (@var "M" tptp.subst) _let_1) (_ tptp.lam (_ (_ _let_1 tptp.sh) tptp.one))))) % 0.39/0.76 (define tptp.hoasvar () (let ((_let_1 (@var "N" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_2 _let_1) (_ tptp.var (_ (_ tptp.sub _let_2) _let_1)))))) % 0.39/0.76 (define tptp.hoasinduction_p_and_p_prime () (let ((_let_1 (@var "X" tptp.term))) (let ((_let_2 (@var "P" (-> tptp.subst tptp.term tptp.subst Bool)))) (let ((_let_3 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (= (_ _let_3 _let_1) (_ (_ (_ _let_2 tptp.id) _let_1) tptp.id)))))))) % 0.39/0.76 (define @t1 () (@var "M" tptp.subst)) % 0.39/0.76 (define @t2 () (@var "B" tptp.term)) % 0.39/0.76 (define @t3 () (_ tptp.sub @t2)) % 0.39/0.76 (define @t4 () (_ @t3 @t1)) % 0.39/0.76 (define @t5 () (@var "A" tptp.term)) % 0.39/0.76 (define @t6 () (_ tptp.sub @t5)) % 0.39/0.76 (define @t7 () (_ @t6 @t1)) % 0.39/0.76 (define @t8 () (_ tptp.ap @t5)) % 0.39/0.76 (define @t9 () (_ @t8 @t2)) % 0.39/0.76 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.39/0.76 (define @t11 () (_ tptp.sub tptp.one)) % 0.39/0.76 (define @t12 () (@list @t5 @t1)) % 0.39/0.76 (define @t13 () (@list @t5)) % 0.39/0.76 (define @t14 () (forall @t13 (= (_ @t6 tptp.id) @t5))) % 0.39/0.76 (define @t15 () (_ tptp.comp @t1)) % 0.39/0.76 (define @t16 () (_ tptp.push tptp.one)) % 0.39/0.76 (define @t17 () (_ tptp.lam @t5)) % 0.39/0.76 (define @t18 () (@var "N" tptp.subst)) % 0.39/0.76 (define @t19 () (_ @t15 @t18)) % 0.39/0.76 (define @t20 () (@list @t5 @t1 @t18)) % 0.39/0.76 (define @t21 () (forall @t20 (= (_ (_ tptp.sub @t7) @t18) (_ @t6 @t19)))) % 0.39/0.76 (define @t22 () (@list @t1)) % 0.39/0.76 (define @t23 () (forall @t22 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 0.39/0.76 (define @t24 () (_ tptp.comp tptp.sh)) % 0.39/0.76 (define @t25 () (@var "K" tptp.subst)) % 0.39/0.76 (define @t26 () (forall (@list @t1 @t18 @t25) (= (_ (_ tptp.comp @t19) @t25) (_ @t15 (_ (_ tptp.comp @t18) @t25))))) % 0.39/0.76 (define @t27 () (_ @t6 @t18)) % 0.39/0.76 (define @t28 () (_ (_ tptp.push @t27) @t19)) % 0.39/0.76 (define @t29 () (forall @t22 (= (_ @t15 tptp.id) @t1))) % 0.39/0.76 (define @t30 () (_ @t16 tptp.sh)) % 0.39/0.76 (define @t31 () (_ @t6 tptp.sh)) % 0.39/0.76 (define @t32 () (_ tptp.var @t5)) % 0.39/0.76 (define @t33 () (@var "P" (-> tptp.term Bool))) % 0.39/0.76 (define @t34 () (_ @t33 @t5)) % 0.39/0.76 (define @t35 () (forall @t13 (=> @t32 @t34))) % 0.39/0.76 (define @t36 () (@list @t33)) % 0.39/0.76 (define @t37 () (= @t5 @t2)) % 0.39/0.76 (define @t38 () (@var "D" tptp.term)) % 0.39/0.76 (define @t39 () (_ tptp.ap @t2)) % 0.39/0.76 (define @t40 () (@var "C" tptp.term)) % 0.39/0.76 (define @t41 () (= (_ @t8 @t40) (_ @t39 @t38))) % 0.39/0.76 (define @t42 () (@list @t5 @t2 @t40 @t38)) % 0.39/0.76 (define @t43 () (= @t40 @t38)) % 0.39/0.76 (define @t44 () (@list @t5 @t2)) % 0.39/0.76 (define @t45 () (forall @t13 @t34)) % 0.39/0.76 (define @t46 () (_ @t33 @t17)) % 0.39/0.76 (define @t47 () (_ @t33 @t2)) % 0.39/0.76 (define @t48 () (forall @t44 (=> @t34 (=> @t47 (_ @t33 @t9))))) % 0.39/0.76 (define @t49 () (@var "Q" (-> tptp.term Bool))) % 0.39/0.76 (define @t50 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t33) @t49)) % 0.39/0.76 (define @t51 () (@list @t49)) % 0.39/0.76 (define @t52 () (@list @t33 @t5 @t1)) % 0.39/0.76 (define @t53 () (_ tptp.push @t2)) % 0.39/0.76 (define @t54 () (@var "K" (-> tptp.term Bool))) % 0.39/0.76 (define @t55 () (@list @t33 @t49 @t5 @t1)) % 0.39/0.76 (define @t56 () (_ tptp.sub @t40)) % 0.39/0.76 (define @t57 () (@list @t40)) % 0.39/0.76 (define @t58 () (_ tptp.var @t2)) % 0.39/0.76 (define @t59 () (@list @t2)) % 0.39/0.76 (define @t60 () (forall @t59 (=> @t58 (_ @t33 @t4)))) % 0.39/0.76 (define @t61 () (_ @t3 @t10)) % 0.39/0.76 (define @t62 () (forall @t59 (=> @t58 (_ @t33 @t61)))) % 0.39/0.76 (define @t63 () (_ @t49 @t2)) % 0.39/0.76 (define @t64 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.39/0.76 (define @t65 () (_ @t6 (_ @t53 tptp.id))) % 0.39/0.76 (define @t66 () (forall @t13 (=> (forall @t59 (=> @t47 (_ @t33 @t65))) @t46))) % 0.39/0.76 (define @t67 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.39/0.76 (define @t68 () (=> tptp.induction2lem tptp.induction2)) % 0.39/0.76 (define @t69 () (_ tptp.hoasap tptp.id)) % 0.39/0.76 (define @t70 () (_ (_ @t69 @t5) tptp.id)) % 0.39/0.76 (define @t71 () (= (_ @t70 @t40) (_ (_ (_ @t69 @t2) tptp.id) @t38))) % 0.39/0.76 (define @t72 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.76 (define @t73 () (_ (_ @t72 @t1) @t5)) % 0.39/0.76 (define @t74 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.76 (define @t75 () (_ @t74 @t1)) % 0.39/0.76 (define @t76 () (_ @t75 @t5)) % 0.39/0.76 (define @t77 () (@list @t1 @t5)) % 0.39/0.76 (define @t78 () (_ tptp.hoaslam tptp.id)) % 0.39/0.76 (define @t79 () (_ @t78 (lambda @t77 @t76))) % 0.39/0.76 (define @t80 () (@list @t1 @t5 @t18)) % 0.39/0.76 (define @t81 () (_ (_ @t74 @t19) @t27)) % 0.39/0.76 (define @t82 () (_ (_ tptp.sub @t76) @t18)) % 0.39/0.76 (define @t83 () (forall @t80 (= @t82 @t81))) % 0.39/0.76 (define @t84 () (@list @t74)) % 0.39/0.76 (define @t85 () (_ @t70 @t2)) % 0.39/0.76 (define @t86 () (_ tptp.hoasvar tptp.id)) % 0.39/0.76 (define @t87 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.39/0.76 (define @t88 () (_ (_ tptp.hoasinduction_p_and_p_prime @t87) @t49)) % 0.39/0.76 (define @t89 () (@list @t87)) % 0.39/0.76 (define @t90 () (_ @t49 @t5)) % 0.39/0.76 (define @t91 () (_ @t87 tptp.id)) % 0.39/0.76 (define @t92 () (_ (_ @t91 @t5) tptp.id)) % 0.39/0.76 (define @t93 () (forall @t13 (=> (_ (_ @t86 @t5) tptp.id) @t92))) % 0.39/0.76 (define @t94 () (_ (_ (_ @t87 @t1) @t5) (_ (_ tptp.comp @t25) @t18))) % 0.39/0.76 (define @t95 () (_ (_ (_ @t87 (_ @t15 @t25)) (_ @t6 @t25)) @t18)) % 0.39/0.76 (define @t96 () (@list @t1 @t5 @t18 @t25)) % 0.39/0.76 (define @t97 () (forall @t96 (=> @t95 @t94))) % 0.39/0.76 (define @t98 () (forall @t96 (=> @t94 @t95))) % 0.39/0.76 (define @t99 () (@list @t87 @t49)) % 0.39/0.76 (define @t100 () (_ (_ @t91 @t2) tptp.id)) % 0.39/0.76 (define @t101 () (forall @t44 (=> @t92 (=> @t100 (_ (_ @t91 @t85) tptp.id))))) % 0.39/0.76 (define @t102 () (=> (forall @t13 (=> @t92 (_ (_ @t91 (_ (_ @t74 tptp.id) @t5)) tptp.id))) (_ (_ @t91 @t79) tptp.id))) % 0.39/0.76 (define @t103 () (forall @t84 (=> @t83 @t102))) % 0.39/0.76 (define @t104 () (=> @t103 (=> @t88 (forall @t13 (=> (forall @t59 (=> @t63 (_ @t49 @t65))) (_ @t49 @t17)))))) % 0.39/0.76 (define @t105 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1))))))))))))))))))))))))))))))))))) % 0.39/0.76 (define @t106 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2))))))))))))))))))))))))))))))))))) % 0.39/0.76 (define @t107 () (forall @t59 (=> @t100 (_ (_ @t91 @t65) tptp.id)))) % 0.39/0.76 (define @t108 () (forall @t13 (=> @t107 (_ (_ @t91 (_ tptp.lam (_ @t6 @t30))) tptp.id)))) % 0.39/0.76 (define @t109 () (=> @t103 (forall @t13 (=> @t107 (_ (_ @t91 @t17) tptp.id))))) % 0.39/0.76 (define @t110 () (_ (_ @t74 tptp.sh) tptp.one)) % 0.39/0.76 (define @t111 () (_ @t3 @t30)) % 0.39/0.76 (define @t112 () (exists @t84 (= @t111 @t110))) % 0.39/0.76 (define @t113 () (forall @t59 @t112)) % 0.39/0.76 (define @t114 () (= tptp.hoasinduction_lem3b @t113)) % 0.39/0.76 (define @t115 () (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.39/0.76 (define @t116 () (=> @t101 (=> @t103 (forall @t13 @t92)))) % 0.39/0.76 (define @t117 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.39/0.76 (define @t118 () (not tptp.hoasinduction_lem3b_lthm)) % 0.39/0.76 (define @t119 () (@var "X" tptp.term)) % 0.39/0.76 (define @t120 () (_ @t49 @t119)) % 0.39/0.76 (define @t121 () (@list @t119)) % 0.39/0.76 (define @t122 () (lambda (@list @t5 @t1 @t33 @t49) (forall @t121 (= @t120 (_ @t33 (_ (_ tptp.sub @t119) @t10)))))) % 0.39/0.76 (define @t123 () (lambda (@list @t1 @t5 @t18 @t2) (_ (_ tptp.ap @t27) @t2))) % 0.39/0.76 (define @t124 () (lambda (@list @t1 @t74) (_ tptp.lam @t110))) % 0.39/0.76 (define @t125 () (lambda @t80 (_ tptp.var @t27))) % 0.39/0.76 (define @t126 () (lambda @t99 (forall @t121 (= @t120 (_ (_ @t91 @t119) tptp.id))))) % 0.39/0.76 (define @t127 () (tptp.push tptp.one tptp.sh)) % 0.39/0.76 (define @t128 () (tptp.sub @t2 @t127)) % 0.39/0.76 (define @t129 () (_ @t74 tptp.sh tptp.one)) % 0.39/0.76 (define @t130 () (= @t110 @t111)) % 0.39/0.76 (define @t131 () (not @t130)) % 0.39/0.76 (define @t132 () (forall @t84 @t131)) % 0.39/0.76 (define @t133 () (not @t132)) % 0.39/0.76 (define @t134 () (forall @t59 (not (forall @t84 (not (= @t129 @t128)))))) % 0.39/0.76 (define @t135 () (@quantifiers_skolemize @t134 0)) % 0.39/0.76 (define @t136 () (tptp.sub @t135 @t127)) % 0.39/0.76 (define @t137 () (forall @t84 (not (= @t129 @t136)))) % 0.39/0.76 (define @t138 () (not @t134)) % 0.39/0.76 (define @t139 () (not (not @t137))) % 0.39/0.76 (define @t140 () (@var "BOUND_VARIABLE_18558" tptp.subst)) % 0.39/0.76 (define @t141 () (@var "BOUND_VARIABLE_18559" tptp.term)) % 0.39/0.76 (define @t142 () (lambda (@list @t140 @t141) (tptp.sub @t135 (tptp.push @t141 @t140)))) % 0.39/0.76 (define @t143 () (= (_ @t142 tptp.sh tptp.one) @t136)) % 0.39/0.76 (define @t144 () (not @t143)) % 0.39/0.76 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.39/0.76 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.39/0.76 (assume @p3 (= tptp.axvarid @t14)) % 0.39/0.76 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t17) @t1) (_ tptp.lam (_ @t6 (_ @t16 (_ @t15 tptp.sh)))))))) % 0.39/0.76 (assume @p5 (= tptp.axclos @t21)) % 0.39/0.76 (assume @p6 (= tptp.axidl @t23)) % 0.39/0.76 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t24 @t10) @t1)))) % 0.39/0.76 (assume @p8 (= tptp.axassoc @t26)) % 0.39/0.76 (assume @p9 (= tptp.axmap (forall @t20 (= (_ (_ tptp.comp @t10) @t18) @t28)))) % 0.39/0.76 (assume @p10 (= tptp.axidr @t29)) % 0.39/0.76 (assume @p11 (= tptp.axvarshift (= @t30 tptp.id))) % 0.39/0.76 (assume @p12 (= tptp.axscons (forall @t22 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t24 @t1)) @t1)))) % 0.39/0.76 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.39/0.76 (assume @p14 (= tptp.ulamvarsh (forall @t13 (=> @t32 (_ tptp.var @t31))))) % 0.39/0.76 (assume @p15 (= tptp.ulamvarind (forall @t36 (=> (_ @t33 tptp.one) (=> (forall @t13 (=> @t32 (=> @t34 (_ @t33 @t31)))) @t35))))) % 0.39/0.76 (assume @p16 (= tptp.apinj1 (forall @t42 (=> @t41 @t37)))) % 0.39/0.76 (assume @p17 (= tptp.apinj2 (forall @t42 (=> @t41 @t43)))) % 0.39/0.76 (assume @p18 (= tptp.laminj (forall @t44 (=> (= @t17 (_ tptp.lam @t2)) @t37)))) % 0.39/0.76 (assume @p19 (= tptp.shinj (forall @t44 (=> (= @t31 (_ @t3 tptp.sh)) @t37)))) % 0.39/0.76 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t40) (not (= @t17 (_ @t39 @t40)))))) % 0.39/0.76 (assume @p21 (= tptp.apnotvar (forall @t44 (not (_ tptp.var @t9))))) % 0.39/0.76 (assume @p22 (= tptp.lamnotvar (forall @t13 (not (_ tptp.var @t17))))) % 0.39/0.76 (assume @p23 (= tptp.induction (forall @t36 (=> @t35 (=> @t48 (=> (forall @t13 (=> @t34 @t46)) @t45)))))) % 0.39/0.76 (assume @p24 (= tptp.pushprop_lem0 (forall @t52 (exists @t51 @t50)))) % 0.39/0.76 (assume @p25 (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0))))))))))))))))))))))))) % 0.39/0.76 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.39/0.76 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t33 @t54 @t5 @t1 @t2) (=> @t34 (_ @t54 (_ @t6 (_ @t53 @t1))))))) % 0.39/0.76 (assume @p28 (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1))))))))))))))))))))))))) % 0.39/0.76 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.39/0.76 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t55 (=> @t34 (=> @t50 (_ @t49 tptp.one)))))) % 0.39/0.76 (assume @p31 (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2))))))))))))))))))))))))) % 0.39/0.76 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.39/0.76 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t55 (=> @t50 (=> @t60 (forall @t57 (=> (_ tptp.var @t40) (=> (_ @t49 @t40) (_ @t49 (_ @t56 tptp.sh)))))))))) % 0.39/0.76 (assume @p34 (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2))))))))))))))))))))))))) % 0.39/0.76 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.39/0.76 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t55 (=> @t50 (=> (forall @t59 (=> @t58 @t63)) @t62))))) % 0.39/0.76 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.39/0.76 (assume @p38 (= tptp.pushprop (forall @t52 (=> @t60 (=> @t34 @t62))))) % 0.39/0.76 (assume @p39 (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop))))))))))))))))))))))))) % 0.39/0.76 (assume @p40 (= tptp.pushprop_lthm_orig @t64)) % 0.39/0.76 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t64))) % 0.39/0.76 (assume @p42 (= tptp.induction2lem (forall @t36 (=> @t48 (=> @t66 (forall @t12 (=> @t60 (_ @t33 @t7)))))))) % 0.39/0.76 (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 @t67)))))))))))))))))))))))) % 0.39/0.76 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t67)))))))))) % 0.39/0.76 (assume @p45 (= tptp.induction2 (forall @t36 (=> @t35 (=> @t48 (=> @t66 @t45)))))) % 0.39/0.76 (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 @t68)))))))))))))))))))))))))) % 0.39/0.76 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t68))) % 0.39/0.76 (assume @p48 (= tptp.substmonoid (and @t26 @t23 @t29))) % 0.39/0.76 (assume @p49 (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid)))))))))))))))))))))))))))) % 0.39/0.76 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.39/0.76 (assume @p51 (= tptp.termmset (and @t21 @t14))) % 0.39/0.76 (assume @p52 (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.39/0.76 (assume @p54 (= tptp.hoasapinj1 (forall @t42 (=> @t71 @t37)))) % 0.39/0.76 (assume @p55 (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1)))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.39/0.76 (assume @p57 (= tptp.hoasapinj2 (forall @t42 (=> @t71 @t43)))) % 0.39/0.76 (assume @p58 (= tptp.hoasapinj2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 tptp.hoasapinj2))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.39/0.76 (assume @p60 (= tptp.hoaslaminj (forall @t84 (=> @t83 (forall (@list @t72) (=> (forall @t80 (= (_ (_ tptp.sub @t73) @t18) (_ (_ @t72 @t19) @t27))) (=> (= @t79 (_ @t78 (lambda @t77 @t73))) (forall @t77 (= @t76 @t73))))))))) % 0.39/0.76 (assume @p61 (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj)))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.39/0.76 (assume @p63 (= tptp.hoaslamnotap (forall @t84 (=> @t83 (forall @t44 (not (= (_ @t78 (lambda (@list @t1 @t40) (_ @t75 @t40))) @t85))))))) % 0.39/0.76 (assume @p64 (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.39/0.76 (assume @p66 (= tptp.hoaslamnotvar (forall @t84 (=> @t83 (not (_ (_ @t86 @t79) tptp.id)))))) % 0.39/0.76 (assume @p67 (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar)))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.39/0.76 (assume @p69 (= tptp.hoasapnotvar (forall @t44 (not (_ (_ @t86 @t85) tptp.id))))) % 0.39/0.76 (assume @p70 (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.39/0.76 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t89 (exists @t51 @t88)))) % 0.39/0.76 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.39/0.76 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t99 (=> @t98 (=> @t97 (=> @t93 (=> @t88 (forall @t13 (=> @t32 @t90))))))))) % 0.39/0.76 (assume @p75 (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t99 (=> @t98 (=> @t97 (=> @t101 (=> @t88 (forall @t44 (=> @t90 (=> @t63 (_ @t49 @t9))))))))))) % 0.39/0.76 (assume @p77 (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t59 (exists @t84 (forall @t12 (= @t76 @t61)))))) % 0.39/0.76 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.39/0.76 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t99 (=> @t98 (=> @t97 @t104))))) % 0.39/0.76 (assume @p81 (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2)))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.39/0.76 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t99 @t104))) % 0.39/0.76 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.39/0.76 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t89 (=> @t98 (=> @t97 (=> @t93 (forall @t13 (=> @t32 @t92)))))))) % 0.39/0.76 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t105)) % 0.39/0.76 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t105)) % 0.39/0.76 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t89 (=> @t98 (=> @t97 (=> @t101 (forall @t44 (=> @t92 (=> @t100 (_ (_ @t91 @t9) tptp.id)))))))))) % 0.39/0.76 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t106)) % 0.39/0.76 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t106)) % 0.39/0.76 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t89 (=> @t103 @t108)))) % 0.39/0.76 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.39/0.76 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t89 (=> (forall @t84 (=> (exists @t57 (forall @t80 (and (= @t82 (_ (_ tptp.sub (_ @t56 @t10)) @t18)) (= (_ @t56 @t28) @t81)))) @t102)) @t108)))) % 0.39/0.76 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t89 (=> @t98 (=> @t97 @t109))))) % 0.39/0.76 (assume @p95 (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3)))))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.39/0.76 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t89 @t109))) % 0.39/0.76 (assume @p98 (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a)))))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.39/0.76 (assume @p100 @t114) % 0.39/0.76 (assume @p101 (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b)))))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p102 @t115) % 0.39/0.76 (assume @p103 (= tptp.hoasinduction (forall @t89 (=> @t98 (=> @t97 (=> @t93 @t116)))))) % 0.39/0.76 (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 @t117)))))))))))))))))))))))))))))))))))) % 0.39/0.76 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t117))) % 0.39/0.76 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.39/0.76 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t89 @t116))) % 0.39/0.76 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.39/0.76 (assume @p109 @t118) % 0.39/0.76 (assume @p110 true) % 0.39/0.76 (step @p111 (= tptp.pushprop_p_and_p_prime @t122) :rule refl :args (@t122)) % 0.39/0.76 (step @p112 (= tptp.hoasap @t123) :rule refl :args (@t123)) % 0.39/0.76 (step @p113 (= tptp.hoaslam @t124) :rule refl :args (@t124)) % 0.39/0.76 (step @p114 (= tptp.hoasvar @t125) :rule refl :args (@t125)) % 0.39/0.76 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t126) :rule refl :args (@t126)) % 0.39/0.76 (step @p116 :rule refl :args ((tptp.sub @t2 @t30))) % 0.39/0.76 (step @p117 :rule refl :args (@t127)) % 0.39/0.76 (step @p118 :rule refl :args (@t2)) % 0.39/0.76 (step @p119 :rule cong :premises (@p118 @p117) :args (@t128)) % 0.39/0.76 (step @p120 :rule trans :premises (@p119 @p116)) % 0.39/0.76 (step @p121 :rule refl :args (@t3)) % 0.39/0.76 (step @p122 :rule ho_cong :premises (@p121 @p117)) % 0.39/0.76 (step @p123 :rule cong :premises (@p122 @p120) :args ((= (_ @t3 @t127) @t128))) % 0.39/0.77 (step @p124 :rule symm :premises (@p123)) % 0.39/0.77 (step @p125 :rule refl :args (@t111)) % 0.39/0.77 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.39/0.77 (step @p127 :rule refl :args (@t30)) % 0.39/0.77 (step @p128 :rule cong :premises (@p127 @p117) :args ((= @t30 @t127))) % 0.39/0.77 (step @p129 :rule symm :premises (@p128)) % 0.39/0.77 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.39/0.77 (step @p131 :rule ho_cong :premises (@p121 @p130)) % 0.39/0.77 (step @p132 :rule trans :premises (@p131 @p126)) % 0.39/0.77 (step @p133 :rule refl :args (@t129)) % 0.39/0.77 (step @p134 :rule refl :args (@t110)) % 0.39/0.77 (step @p135 :rule cong :premises (@p134 @p133) :args ((= @t110 @t129))) % 0.39/0.77 (step @p136 :rule symm :premises (@p135)) % 0.39/0.77 (step @p137 :rule eq_resolve :premises (@p134 @p136)) % 0.39/0.77 (step @p138 :rule cong :premises (@p137 @p132) :args (@t130)) % 0.39/0.77 (step @p139 :rule cong :premises (@p138) :args (@t131)) % 0.39/0.77 (step @p140 :rule cong :premises (@p139) :args (@t132)) % 0.39/0.77 (step @p141 :rule cong :premises (@p140) :args (@t133)) % 0.39/0.77 (step @p142 :rule exists-elim :args ((= (exists @t84 @t130) @t133))) % 0.39/0.77 (step @p143 :rule trans :premises (@p142 @p141)) % 0.39/0.77 (step @p144 :rule eq-symm :args (@t111 @t110)) % 0.39/0.77 (step @p145 :rule cong :premises (@p144) :args (@t112)) % 0.39/0.77 (step @p146 :rule trans :premises (@p145 @p143)) % 0.39/0.77 (step @p147 :rule cong :premises (@p146) :args (@t113)) % 0.39/0.77 (step @p148 :rule refl :args (tptp.hoasinduction_lem3b)) % 0.39/0.77 (step @p149 :rule cong :premises (@p148 @p147) :args (@t114)) % 0.39/0.77 (step @p150 :rule eq_resolve :premises (@p100 @p149)) % 0.39/0.77 (step @p151 :rule refl :args (tptp.hoasinduction_lem3b_lthm)) % 0.39/0.77 (step @p152 :rule cong :premises (@p151 @p150) :args (@t115)) % 0.39/0.77 (step @p153 :rule eq_resolve :premises (@p102 @p152)) % 0.39/0.77 (step @p154 :rule cong :premises (@p153) :args (@t118)) % 0.39/0.77 (step @p155 :rule eq_resolve :premises (@p109 @p154)) % 0.39/0.77 (step @p156 :rule refl :args (@t137)) % 0.39/0.77 (step @p157 :rule bool-double-not-elim :args (@t134)) % 0.39/0.77 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or (not @t138) @t137))) % 0.39/0.77 (step @p159 :rule bool-double-not-elim :args (@t137)) % 0.39/0.77 (step @p160 :rule refl :args (@t138)) % 0.39/0.77 (step @p161 :rule cong :premises (@p160 @p159) :args ((=> @t138 @t139))) % 0.39/0.77 (assume-push @p187 @t138) % 0.39/0.77 (step @p163 :rule skolemize :premises (@p155)) % 0.39/0.77 (step-pop @p188 :rule scope :premises (@p163)) % 0.39/0.77 (step @p164 :rule process_scope :premises (@p188) :args (@t139)) % 0.39/0.77 (step @p166 :rule eq_resolve :premises (@p164 @p161)) % 0.39/0.77 (step @p167 :rule implies_elim :premises (@p166)) % 0.39/0.77 (step @p168 :rule eq_resolve :premises (@p167 @p158)) % 0.39/0.77 (step @p169 :rule chain_m_resolution :premises (@p168 @p155) :args (@t137 (@list true) (@list @t134))) % 0.39/0.77 (step @p170 :rule bool-impl-false1 :args (@t137)) % 0.39/0.77 (step @p171 :rule evaluate :args ((not true))) % 0.39/0.77 (step @p172 :rule eq-refl :args (@t136)) % 0.39/0.77 (step @p173 :rule refl :args (@t136)) % 0.39/0.77 (step @p174 :rule beta-reduce :args (@t143)) % 0.39/0.77 (step @p175 :rule cong :premises (@p174 @p173) :args (@t143)) % 0.39/0.77 (step @p176 :rule trans :premises (@p175 @p172)) % 0.39/0.77 (step @p177 :rule cong :premises (@p176) :args (@t144)) % 0.39/0.77 (step @p178 :rule trans :premises (@p177 @p171)) % 0.39/0.77 (step @p179 :rule cong :premises (@p156 @p178) :args ((=> @t137 @t144))) % 0.39/0.77 (step @p180 :rule trans :premises (@p179 @p170)) % 0.39/0.77 (assume-push @p189 @t137) % 0.39/0.77 (step @p182 :rule instantiate :premises (@p169) :args ((@list @t142))) % 0.39/0.77 (step-pop @p190 :rule scope :premises (@p182)) % 0.39/0.77 (step @p183 :rule process_scope :premises (@p190) :args (@t144)) % 0.39/0.77 (step @p185 :rule eq_resolve :premises (@p183 @p180)) % 0.39/0.77 (step @p186 false :rule chain_m_resolution :premises (@p185 @p169) :args (false (@list false) (@list @t137))) % 0.39/0.77 ) % 0.39/0.77 % SZS output end Proof % 0.39/0.77 % cvc5 exiting %------------------------------------------------------------------------------