%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG254^2 : 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 : n004.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 0.39s 0.68s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG254^2 : 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 % 0.17/0.34 % Computer : n004.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 01:55:07 EDT 2026 % 0.17/0.35 % CPUTime : % 0.38/0.55 %----Proving TH0 % 0.39/0.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.68 % SZS status Theorem % 0.39/0.68 % SZS output start Proof % 0.39/0.68 ( % 0.39/0.68 (declare-sort tptp.term 0) % 0.39/0.68 (declare-sort tptp.subst 0) % 0.39/0.68 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.39/0.68 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.39/0.68 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.39/0.68 (declare-const tptp.one tptp.term) % 0.39/0.68 (declare-const tptp.sh tptp.subst) % 0.39/0.68 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.39/0.68 (declare-const tptp.var (-> tptp.term Bool)) % 0.39/0.68 (declare-const tptp.id tptp.subst) % 0.39/0.68 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3b Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3a Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem0 Bool) % 0.39/0.68 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasapnotvar Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotvar Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotap Bool) % 0.39/0.68 (declare-const tptp.hoaslaminj_lthm Bool) % 0.39/0.68 (declare-const tptp.hoaslaminj_gthm Bool) % 0.39/0.68 (declare-const tptp.hoaslaminj Bool) % 0.39/0.68 (declare-const tptp.hoasapinj2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasapinj2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasapinj2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.39/0.68 (declare-const tptp.axassoc Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.39/0.68 (declare-const tptp.axvarcons Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem0 Bool) % 0.39/0.68 (declare-const tptp.apinj1 Bool) % 0.39/0.68 (declare-const tptp.induction Bool) % 0.39/0.68 (declare-const tptp.apnotvar Bool) % 0.39/0.68 (declare-const tptp.laminj Bool) % 0.39/0.68 (declare-const tptp.axvarshift Bool) % 0.39/0.68 (declare-const tptp.ulamvarind Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.39/0.68 (declare-const tptp.ulamvarsh Bool) % 0.39/0.68 (declare-const tptp.ulamvar1 Bool) % 0.39/0.68 (declare-const tptp.axabs Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1 Bool) % 0.39/0.68 (declare-const tptp.shinj Bool) % 0.39/0.68 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.39/0.68 (declare-const tptp.apinj2 Bool) % 0.39/0.68 (declare-const tptp.axvarid Bool) % 0.39/0.68 (declare-const tptp.axidl Bool) % 0.39/0.68 (declare-const tptp.axclos Bool) % 0.39/0.68 (declare-const tptp.termmset Bool) % 0.39/0.68 (declare-const tptp.axshiftcons Bool) % 0.39/0.68 (declare-const tptp.lamnotap Bool) % 0.39/0.68 (declare-const tptp.lamnotvar Bool) % 0.39/0.68 (declare-const tptp.axapp Bool) % 0.39/0.68 (declare-const tptp.axscons Bool) % 0.39/0.68 (declare-const tptp.axmap Bool) % 0.39/0.68 (declare-const tptp.axidr Bool) % 0.39/0.68 (declare-const tptp.induction2lem Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasapinj1_lthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1v2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.39/0.68 (declare-const tptp.induction2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem2v2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem3v2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.39/0.68 (declare-const tptp.pushprop Bool) % 0.39/0.68 (declare-const tptp.pushprop_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasapinj1 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lthm_orig Bool) % 0.39/0.68 (declare-const tptp.pushprop_lthm Bool) % 0.39/0.68 (declare-const tptp.induction2lem_gthm Bool) % 0.39/0.68 (declare-const tptp.induction2lem_lthm Bool) % 0.39/0.68 (declare-const tptp.induction2_gthm Bool) % 0.39/0.68 (declare-const tptp.induction2_lthm Bool) % 0.39/0.68 (declare-const tptp.substmonoid Bool) % 0.39/0.68 (declare-const tptp.substmonoid_gthm Bool) % 0.39/0.68 (declare-const tptp.termmset_gthm Bool) % 0.39/0.68 (declare-const tptp.substmonoid_lthm Bool) % 0.39/0.68 (declare-const tptp.termmset_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasapinj1_gthm Bool) % 0.39/0.68 (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)))))))))))) % 0.39/0.68 (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)))))) % 0.39/0.68 (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))))) % 0.39/0.68 (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)))))) % 0.39/0.68 (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)))))))) % 0.39/0.68 (define @t1 () (@var "M" tptp.subst)) % 0.39/0.68 (define @t2 () (@var "B" tptp.term)) % 0.39/0.68 (define @t3 () (_ tptp.sub @t2)) % 0.39/0.68 (define @t4 () (_ @t3 @t1)) % 0.39/0.68 (define @t5 () (@var "A" tptp.term)) % 0.39/0.68 (define @t6 () (_ tptp.sub @t5)) % 0.39/0.68 (define @t7 () (_ @t6 @t1)) % 0.39/0.68 (define @t8 () (_ tptp.ap @t5)) % 0.39/0.68 (define @t9 () (_ @t8 @t2)) % 0.39/0.68 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.39/0.68 (define @t11 () (_ tptp.sub tptp.one)) % 0.39/0.68 (define @t12 () (@list @t5 @t1)) % 0.39/0.68 (define @t13 () (@list @t5)) % 0.39/0.68 (define @t14 () (forall @t13 (= (_ @t6 tptp.id) @t5))) % 0.39/0.68 (define @t15 () (_ tptp.comp @t1)) % 0.39/0.68 (define @t16 () (_ tptp.push tptp.one)) % 0.39/0.68 (define @t17 () (_ tptp.lam @t5)) % 0.39/0.68 (define @t18 () (@var "N" tptp.subst)) % 0.39/0.68 (define @t19 () (_ @t15 @t18)) % 0.39/0.68 (define @t20 () (@list @t5 @t1 @t18)) % 0.39/0.68 (define @t21 () (forall @t20 (= (_ (_ tptp.sub @t7) @t18) (_ @t6 @t19)))) % 0.39/0.68 (define @t22 () (_ (_ tptp.comp tptp.id) @t1)) % 0.39/0.68 (define @t23 () (@list @t1)) % 0.39/0.68 (define @t24 () (forall @t23 (= @t22 @t1))) % 0.39/0.68 (define @t25 () (= tptp.axidl @t24)) % 0.39/0.68 (define @t26 () (_ tptp.comp tptp.sh)) % 0.39/0.68 (define @t27 () (@var "K" tptp.subst)) % 0.39/0.68 (define @t28 () (_ (_ tptp.comp @t18) @t27)) % 0.39/0.68 (define @t29 () (_ @t15 @t28)) % 0.39/0.68 (define @t30 () (_ (_ tptp.comp @t19) @t27)) % 0.39/0.68 (define @t31 () (= @t30 @t29)) % 0.39/0.68 (define @t32 () (forall (@list @t1 @t18 @t27) @t31)) % 0.39/0.68 (define @t33 () (= tptp.axassoc @t32)) % 0.39/0.68 (define @t34 () (_ @t6 @t18)) % 0.39/0.68 (define @t35 () (_ (_ tptp.push @t34) @t19)) % 0.39/0.68 (define @t36 () (_ @t15 tptp.id)) % 0.39/0.68 (define @t37 () (forall @t23 (= @t36 @t1))) % 0.39/0.68 (define @t38 () (= tptp.axidr @t37)) % 0.39/0.68 (define @t39 () (_ @t16 tptp.sh)) % 0.39/0.68 (define @t40 () (_ @t6 tptp.sh)) % 0.39/0.68 (define @t41 () (_ tptp.var @t5)) % 0.39/0.68 (define @t42 () (@var "P" (-> tptp.term Bool))) % 0.39/0.68 (define @t43 () (_ @t42 @t5)) % 0.39/0.68 (define @t44 () (forall @t13 (=> @t41 @t43))) % 0.39/0.68 (define @t45 () (@list @t42)) % 0.39/0.68 (define @t46 () (= @t5 @t2)) % 0.39/0.68 (define @t47 () (@var "D" tptp.term)) % 0.39/0.68 (define @t48 () (_ tptp.ap @t2)) % 0.39/0.68 (define @t49 () (@var "C" tptp.term)) % 0.39/0.68 (define @t50 () (= (_ @t8 @t49) (_ @t48 @t47))) % 0.39/0.68 (define @t51 () (@list @t5 @t2 @t49 @t47)) % 0.39/0.68 (define @t52 () (= @t49 @t47)) % 0.39/0.68 (define @t53 () (@list @t5 @t2)) % 0.39/0.68 (define @t54 () (forall @t13 @t43)) % 0.39/0.68 (define @t55 () (_ @t42 @t17)) % 0.39/0.68 (define @t56 () (_ @t42 @t2)) % 0.39/0.68 (define @t57 () (forall @t53 (=> @t43 (=> @t56 (_ @t42 @t9))))) % 0.39/0.68 (define @t58 () (@var "Q" (-> tptp.term Bool))) % 0.39/0.68 (define @t59 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t42) @t58)) % 0.39/0.68 (define @t60 () (@list @t58)) % 0.39/0.68 (define @t61 () (@list @t42 @t5 @t1)) % 0.39/0.68 (define @t62 () (_ tptp.push @t2)) % 0.39/0.68 (define @t63 () (@var "K" (-> tptp.term Bool))) % 0.39/0.68 (define @t64 () (@list @t42 @t58 @t5 @t1)) % 0.39/0.68 (define @t65 () (_ tptp.sub @t49)) % 0.39/0.68 (define @t66 () (@list @t49)) % 0.39/0.68 (define @t67 () (_ tptp.var @t2)) % 0.39/0.68 (define @t68 () (@list @t2)) % 0.39/0.68 (define @t69 () (forall @t68 (=> @t67 (_ @t42 @t4)))) % 0.39/0.68 (define @t70 () (_ @t3 @t10)) % 0.39/0.68 (define @t71 () (forall @t68 (=> @t67 (_ @t42 @t70)))) % 0.39/0.68 (define @t72 () (_ @t58 @t2)) % 0.39/0.68 (define @t73 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.39/0.68 (define @t74 () (_ @t6 (_ @t62 tptp.id))) % 0.39/0.68 (define @t75 () (forall @t13 (=> (forall @t68 (=> @t56 (_ @t42 @t74))) @t55))) % 0.39/0.68 (define @t76 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.39/0.68 (define @t77 () (=> tptp.induction2lem tptp.induction2)) % 0.39/0.68 (define @t78 () (and @t32 @t24 @t37)) % 0.39/0.68 (define @t79 () (= tptp.substmonoid @t78)) % 0.39/0.68 (define @t80 () (_ tptp.hoasap tptp.id)) % 0.39/0.68 (define @t81 () (_ (_ @t80 @t5) tptp.id)) % 0.39/0.68 (define @t82 () (= (_ @t81 @t49) (_ (_ (_ @t80 @t2) tptp.id) @t47))) % 0.39/0.68 (define @t83 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.68 (define @t84 () (_ (_ @t83 @t1) @t5)) % 0.39/0.68 (define @t85 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.68 (define @t86 () (_ @t85 @t1)) % 0.39/0.68 (define @t87 () (_ @t86 @t5)) % 0.39/0.68 (define @t88 () (@list @t1 @t5)) % 0.39/0.68 (define @t89 () (_ tptp.hoaslam tptp.id)) % 0.39/0.68 (define @t90 () (_ @t89 (lambda @t88 @t87))) % 0.39/0.68 (define @t91 () (@list @t1 @t5 @t18)) % 0.39/0.68 (define @t92 () (_ (_ @t85 @t19) @t34)) % 0.39/0.68 (define @t93 () (_ (_ tptp.sub @t87) @t18)) % 0.39/0.68 (define @t94 () (forall @t91 (= @t93 @t92))) % 0.39/0.68 (define @t95 () (@list @t85)) % 0.39/0.68 (define @t96 () (_ @t81 @t2)) % 0.39/0.68 (define @t97 () (_ tptp.hoasvar tptp.id)) % 0.39/0.68 (define @t98 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.39/0.68 (define @t99 () (_ (_ tptp.hoasinduction_p_and_p_prime @t98) @t58)) % 0.39/0.68 (define @t100 () (@list @t98)) % 0.39/0.68 (define @t101 () (_ @t58 @t5)) % 0.39/0.68 (define @t102 () (_ @t98 tptp.id)) % 0.39/0.68 (define @t103 () (_ (_ @t102 @t5) tptp.id)) % 0.39/0.68 (define @t104 () (forall @t13 (=> (_ (_ @t97 @t5) tptp.id) @t103))) % 0.39/0.68 (define @t105 () (_ (_ (_ @t98 @t1) @t5) (_ (_ tptp.comp @t27) @t18))) % 0.39/0.68 (define @t106 () (_ (_ (_ @t98 (_ @t15 @t27)) (_ @t6 @t27)) @t18)) % 0.39/0.68 (define @t107 () (@list @t1 @t5 @t18 @t27)) % 0.39/0.68 (define @t108 () (forall @t107 (=> @t106 @t105))) % 0.39/0.68 (define @t109 () (forall @t107 (=> @t105 @t106))) % 0.39/0.68 (define @t110 () (@list @t98 @t58)) % 0.39/0.68 (define @t111 () (_ (_ @t102 @t2) tptp.id)) % 0.39/0.68 (define @t112 () (forall @t53 (=> @t103 (=> @t111 (_ (_ @t102 @t96) tptp.id))))) % 0.39/0.68 (define @t113 () (=> (forall @t13 (=> @t103 (_ (_ @t102 (_ (_ @t85 tptp.id) @t5)) tptp.id))) (_ (_ @t102 @t90) tptp.id))) % 0.39/0.68 (define @t114 () (forall @t95 (=> @t94 @t113))) % 0.39/0.68 (define @t115 () (=> @t114 (=> @t99 (forall @t13 (=> (forall @t68 (=> @t72 (_ @t58 @t74))) (_ @t58 @t17)))))) % 0.39/0.68 (define @t116 () (=> 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))))))))))))))))))))))))))))))))))) % 0.39/0.68 (define @t117 () (=> 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))))))))))))))))))))))))))))))))))) % 0.39/0.68 (define @t118 () (forall @t68 (=> @t111 (_ (_ @t102 @t74) tptp.id)))) % 0.39/0.68 (define @t119 () (forall @t13 (=> @t118 (_ (_ @t102 (_ tptp.lam (_ @t6 @t39))) tptp.id)))) % 0.39/0.68 (define @t120 () (=> @t114 (forall @t13 (=> @t118 (_ (_ @t102 @t17) tptp.id))))) % 0.39/0.68 (define @t121 () (_ (_ @t85 tptp.sh) tptp.one)) % 0.39/0.68 (define @t122 () (=> @t112 (=> @t114 (forall @t13 @t103)))) % 0.39/0.68 (define @t123 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.39/0.68 (define @t124 () (@var "X" tptp.term)) % 0.39/0.68 (define @t125 () (_ @t58 @t124)) % 0.39/0.68 (define @t126 () (@list @t124)) % 0.39/0.68 (define @t127 () (lambda (@list @t5 @t1 @t42 @t58) (forall @t126 (= @t125 (_ @t42 (_ (_ tptp.sub @t124) @t10)))))) % 0.39/0.68 (define @t128 () (lambda (@list @t1 @t5 @t18 @t2) (_ (_ tptp.ap @t34) @t2))) % 0.39/0.68 (define @t129 () (lambda (@list @t1 @t85) (_ tptp.lam @t121))) % 0.39/0.68 (define @t130 () (lambda @t91 (_ tptp.var @t34))) % 0.39/0.68 (define @t131 () (lambda @t110 (forall @t126 (= @t125 (_ (_ @t102 @t124) tptp.id))))) % 0.39/0.68 (define @t132 () (tptp.comp @t1 tptp.id)) % 0.39/0.68 (define @t133 () (= @t1 @t36)) % 0.39/0.68 (define @t134 () (tptp.comp tptp.id @t1)) % 0.39/0.68 (define @t135 () (= @t1 @t22)) % 0.39/0.68 (define @t136 () (tptp.comp @t18 @t27)) % 0.39/0.68 (define @t137 () (tptp.comp @t1 @t136)) % 0.39/0.68 (define @t138 () (tptp.comp @t1 @t18)) % 0.39/0.68 (define @t139 () (tptp.comp @t138 @t27)) % 0.39/0.68 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.39/0.68 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.39/0.68 (assume @p3 (= tptp.axvarid @t14)) % 0.39/0.68 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t17) @t1) (_ tptp.lam (_ @t6 (_ @t16 (_ @t15 tptp.sh)))))))) % 0.39/0.68 (assume @p5 (= tptp.axclos @t21)) % 0.39/0.68 (assume @p6 @t25) % 0.39/0.68 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t26 @t10) @t1)))) % 0.39/0.68 (assume @p8 @t33) % 0.39/0.68 (assume @p9 (= tptp.axmap (forall @t20 (= (_ (_ tptp.comp @t10) @t18) @t35)))) % 0.39/0.68 (assume @p10 @t38) % 0.39/0.68 (assume @p11 (= tptp.axvarshift (= @t39 tptp.id))) % 0.39/0.68 (assume @p12 (= tptp.axscons (forall @t23 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t26 @t1)) @t1)))) % 0.39/0.68 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.39/0.68 (assume @p14 (= tptp.ulamvarsh (forall @t13 (=> @t41 (_ tptp.var @t40))))) % 0.39/0.68 (assume @p15 (= tptp.ulamvarind (forall @t45 (=> (_ @t42 tptp.one) (=> (forall @t13 (=> @t41 (=> @t43 (_ @t42 @t40)))) @t44))))) % 0.39/0.68 (assume @p16 (= tptp.apinj1 (forall @t51 (=> @t50 @t46)))) % 0.39/0.68 (assume @p17 (= tptp.apinj2 (forall @t51 (=> @t50 @t52)))) % 0.39/0.68 (assume @p18 (= tptp.laminj (forall @t53 (=> (= @t17 (_ tptp.lam @t2)) @t46)))) % 0.39/0.68 (assume @p19 (= tptp.shinj (forall @t53 (=> (= @t40 (_ @t3 tptp.sh)) @t46)))) % 0.39/0.68 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t49) (not (= @t17 (_ @t48 @t49)))))) % 0.39/0.68 (assume @p21 (= tptp.apnotvar (forall @t53 (not (_ tptp.var @t9))))) % 0.39/0.68 (assume @p22 (= tptp.lamnotvar (forall @t13 (not (_ tptp.var @t17))))) % 0.39/0.68 (assume @p23 (= tptp.induction (forall @t45 (=> @t44 (=> @t57 (=> (forall @t13 (=> @t43 @t55)) @t54)))))) % 0.39/0.68 (assume @p24 (= tptp.pushprop_lem0 (forall @t61 (exists @t60 @t59)))) % 0.39/0.68 (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))))))))))))))))))))))))) % 0.39/0.68 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.39/0.68 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t42 @t63 @t5 @t1 @t2) (=> @t43 (_ @t63 (_ @t6 (_ @t62 @t1))))))) % 0.39/0.68 (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))))))))))))))))))))))))) % 0.39/0.68 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.39/0.68 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t64 (=> @t43 (=> @t59 (_ @t58 tptp.one)))))) % 0.39/0.68 (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))))))))))))))))))))))))) % 0.39/0.68 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.39/0.68 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t64 (=> @t59 (=> @t69 (forall @t66 (=> (_ tptp.var @t49) (=> (_ @t58 @t49) (_ @t58 (_ @t65 tptp.sh)))))))))) % 0.39/0.68 (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))))))))))))))))))))))))) % 0.39/0.68 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.39/0.68 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t64 (=> @t59 (=> (forall @t68 (=> @t67 @t72)) @t71))))) % 0.39/0.68 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.39/0.68 (assume @p38 (= tptp.pushprop (forall @t61 (=> @t69 (=> @t43 @t71))))) % 0.39/0.68 (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))))))))))))))))))))))))) % 0.39/0.68 (assume @p40 (= tptp.pushprop_lthm_orig @t73)) % 0.39/0.68 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t73))) % 0.39/0.68 (assume @p42 (= tptp.induction2lem (forall @t45 (=> @t57 (=> @t75 (forall @t12 (=> @t69 (_ @t42 @t7)))))))) % 0.39/0.68 (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 @t76)))))))))))))))))))))))) % 0.39/0.68 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t76)))))))))) % 0.39/0.68 (assume @p45 (= tptp.induction2 (forall @t45 (=> @t44 (=> @t57 (=> @t75 @t54)))))) % 0.39/0.68 (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 @t77)))))))))))))))))))))))))) % 0.39/0.68 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t77))) % 0.39/0.68 (assume @p48 @t79) % 0.39/0.68 (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)))))))))))))))))))))))))))) % 0.39/0.68 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.39/0.68 (assume @p51 (= tptp.termmset (and @t21 @t14))) % 0.39/0.68 (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))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.39/0.68 (assume @p54 (= tptp.hoasapinj1 (forall @t51 (=> @t82 @t46)))) % 0.39/0.68 (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)))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.39/0.68 (assume @p57 (= tptp.hoasapinj2 (forall @t51 (=> @t82 @t52)))) % 0.39/0.68 (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))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.39/0.68 (assume @p60 (= tptp.hoaslaminj (forall @t95 (=> @t94 (forall (@list @t83) (=> (forall @t91 (= (_ (_ tptp.sub @t84) @t18) (_ (_ @t83 @t19) @t34))) (=> (= @t90 (_ @t89 (lambda @t88 @t84))) (forall @t88 (= @t87 @t84))))))))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.39/0.68 (assume @p63 (= tptp.hoaslamnotap (forall @t95 (=> @t94 (forall @t53 (not (= (_ @t89 (lambda (@list @t1 @t49) (_ @t86 @t49))) @t96))))))) % 0.39/0.68 (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))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.39/0.68 (assume @p66 (= tptp.hoaslamnotvar (forall @t95 (=> @t94 (not (_ (_ @t97 @t90) tptp.id)))))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.39/0.68 (assume @p69 (= tptp.hoasapnotvar (forall @t53 (not (_ (_ @t97 @t96) tptp.id))))) % 0.39/0.68 (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))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.39/0.68 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t100 (exists @t60 @t99)))) % 0.39/0.68 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.39/0.68 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t110 (=> @t109 (=> @t108 (=> @t104 (=> @t99 (forall @t13 (=> @t41 @t101))))))))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t110 (=> @t109 (=> @t108 (=> @t112 (=> @t99 (forall @t53 (=> @t101 (=> @t72 (_ @t58 @t9))))))))))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t68 (exists @t95 (forall @t12 (= @t87 @t70)))))) % 0.39/0.68 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.39/0.68 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t110 (=> @t109 (=> @t108 @t115))))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.39/0.68 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t110 @t115))) % 0.39/0.68 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.39/0.68 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t100 (=> @t109 (=> @t108 (=> @t104 (forall @t13 (=> @t41 @t103)))))))) % 0.39/0.68 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t116)) % 0.39/0.68 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t116)) % 0.39/0.68 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t100 (=> @t109 (=> @t108 (=> @t112 (forall @t53 (=> @t103 (=> @t111 (_ (_ @t102 @t9) tptp.id)))))))))) % 0.39/0.68 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t117)) % 0.39/0.68 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t117)) % 0.39/0.68 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t100 (=> @t114 @t119)))) % 0.39/0.68 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.39/0.68 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t100 (=> (forall @t95 (=> (exists @t66 (forall @t91 (and (= @t93 (_ (_ tptp.sub (_ @t65 @t10)) @t18)) (= (_ @t65 @t35) @t92)))) @t113)) @t119)))) % 0.39/0.68 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t100 (=> @t109 (=> @t108 @t120))))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.39/0.68 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t100 @t120))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.39/0.68 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t68 (exists @t95 (= (_ @t3 @t39) @t121))))) % 0.39/0.68 (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)))))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.39/0.68 (assume @p103 (= tptp.hoasinduction (forall @t100 (=> @t109 (=> @t108 (=> @t104 @t122)))))) % 0.39/0.68 (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 @t123)))))))))))))))))))))))))))))))))))) % 0.39/0.68 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t123))) % 0.39/0.68 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.39/0.68 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t100 @t122))) % 0.39/0.68 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.39/0.68 (assume @p109 (not tptp.substmonoid_lthm)) % 0.39/0.68 (assume @p110 true) % 0.39/0.68 (step @p111 (= tptp.pushprop_p_and_p_prime @t127) :rule refl :args (@t127)) % 0.39/0.68 (step @p112 (= tptp.hoasap @t128) :rule refl :args (@t128)) % 0.39/0.68 (step @p113 (= tptp.hoaslam @t129) :rule refl :args (@t129)) % 0.39/0.68 (step @p114 (= tptp.hoasvar @t130) :rule refl :args (@t130)) % 0.39/0.68 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t131) :rule refl :args (@t131)) % 0.39/0.68 (step @p116 :rule equiv_elim2 :premises (@p50)) % 0.39/0.68 (step @p117 :rule resolution :premises (@p116 @p109) :args (true tptp.substmonoid_lthm)) % 0.39/0.68 (step @p118 :rule not_implies_elim2 :premises (@p117)) % 0.39/0.68 (step @p119 :rule not_implies_elim2 :premises (@p118)) % 0.39/0.68 (step @p120 :rule not_implies_elim2 :premises (@p119)) % 0.39/0.68 (step @p121 :rule refl :args (@t132)) % 0.39/0.68 (step @p122 :rule refl :args (@t36)) % 0.39/0.68 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t36 @t132))) % 0.39/0.68 (step @p124 :rule symm :premises (@p123)) % 0.39/0.68 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 0.39/0.68 (step @p126 :rule refl :args (@t1)) % 0.39/0.68 (step @p127 :rule cong :premises (@p126 @p125) :args (@t133)) % 0.39/0.68 (step @p128 :rule cong :premises (@p127) :args ((forall @t23 @t133))) % 0.39/0.68 (step @p129 :rule eq-symm :args (@t36 @t1)) % 0.39/0.68 (step @p130 :rule cong :premises (@p129) :args (@t37)) % 0.39/0.68 (step @p131 :rule trans :premises (@p130 @p128)) % 0.39/0.68 (step @p132 :rule refl :args (@t134)) % 0.39/0.68 (step @p133 :rule refl :args (@t22)) % 0.39/0.68 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t22 @t134))) % 0.39/0.68 (step @p135 :rule symm :premises (@p134)) % 0.39/0.68 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.39/0.68 (step @p137 :rule cong :premises (@p126 @p136) :args (@t135)) % 0.39/0.68 (step @p138 :rule cong :premises (@p137) :args ((forall @t23 @t135))) % 0.39/0.68 (step @p139 :rule eq-symm :args (@t22 @t1)) % 0.39/0.68 (step @p140 :rule cong :premises (@p139) :args (@t24)) % 0.39/0.68 (step @p141 :rule trans :premises (@p140 @p138)) % 0.39/0.68 (step @p142 :rule refl :args ((tptp.comp @t1 @t28))) % 0.39/0.68 (step @p143 :rule refl :args (@t136)) % 0.39/0.68 (step @p144 :rule cong :premises (@p126 @p143) :args (@t137)) % 0.39/0.68 (step @p145 :rule trans :premises (@p144 @p142)) % 0.39/0.68 (step @p146 :rule refl :args (@t15)) % 0.39/0.68 (step @p147 :rule ho_cong :premises (@p146 @p143)) % 0.39/0.68 (step @p148 :rule cong :premises (@p147 @p145) :args ((= (_ @t15 @t136) @t137))) % 0.39/0.68 (step @p149 :rule symm :premises (@p148)) % 0.39/0.68 (step @p150 :rule refl :args (@t29)) % 0.39/0.68 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.39/0.68 (step @p152 :rule refl :args (@t28)) % 0.39/0.68 (step @p153 :rule cong :premises (@p152 @p143) :args ((= @t28 @t136))) % 0.39/0.68 (step @p154 :rule symm :premises (@p153)) % 0.39/0.68 (step @p155 :rule eq_resolve :premises (@p152 @p154)) % 0.39/0.68 (step @p156 :rule ho_cong :premises (@p146 @p155)) % 0.39/0.68 (step @p157 :rule trans :premises (@p156 @p151)) % 0.39/0.68 (step @p158 :rule refl :args ((tptp.comp @t19 @t27))) % 0.39/0.68 (step @p159 :rule refl :args (@t27)) % 0.39/0.68 (step @p160 :rule refl :args (@t138)) % 0.39/0.68 (step @p161 :rule cong :premises (@p160 @p159) :args (@t139)) % 0.39/0.68 (step @p162 :rule trans :premises (@p161 @p158)) % 0.39/0.68 (step @p163 :rule refl :args (tptp.comp)) % 0.39/0.68 (step @p164 :rule ho_cong :premises (@p163 @p160)) % 0.39/0.68 (step @p165 :rule ho_cong :premises (@p164 @p159)) % 0.39/0.68 (step @p166 :rule cong :premises (@p165 @p162) :args ((= (_ (_ tptp.comp @t138) @t27) @t139))) % 0.39/0.68 (step @p167 :rule symm :premises (@p166)) % 0.39/0.68 (step @p168 :rule refl :args (@t30)) % 0.39/0.68 (step @p169 :rule eq_resolve :premises (@p168 @p167)) % 0.39/0.68 (step @p170 :rule refl :args (@t19)) % 0.39/0.68 (step @p171 :rule cong :premises (@p170 @p160) :args ((= @t19 @t138))) % 0.39/0.68 (step @p172 :rule symm :premises (@p171)) % 0.39/0.68 (step @p173 :rule eq_resolve :premises (@p170 @p172)) % 0.39/0.68 (step @p174 :rule ho_cong :premises (@p163 @p173)) % 0.39/0.68 (step @p175 :rule ho_cong :premises (@p174 @p159)) % 0.39/0.68 (step @p176 :rule trans :premises (@p175 @p169)) % 0.39/0.68 (step @p177 :rule cong :premises (@p176 @p157) :args (@t31)) % 0.39/0.68 (step @p178 :rule cong :premises (@p177) :args (@t32)) % 0.39/0.68 (step @p179 :rule nary_cong :premises (@p178 @p141 @p131) :args (@t78)) % 0.39/0.68 (step @p180 :rule refl :args (tptp.substmonoid)) % 0.39/0.68 (step @p181 :rule cong :premises (@p180 @p179) :args (@t79)) % 0.39/0.68 (step @p182 :rule eq_resolve :premises (@p48 @p181)) % 0.39/0.68 (step @p183 :rule equiv_elim2 :premises (@p182)) % 0.39/0.68 (step @p184 :rule resolution :premises (@p183 @p120) :args (true tptp.substmonoid)) % 0.39/0.68 (step @p185 :rule refl :args (tptp.axidr)) % 0.39/0.68 (step @p186 :rule cong :premises (@p185 @p131) :args (@t38)) % 0.39/0.68 (step @p187 :rule eq_resolve :premises (@p10 @p186)) % 0.39/0.68 (step @p188 :rule not_implies_elim1 :premises (@p119)) % 0.39/0.68 (step @p189 :rule eq_resolve :premises (@p188 @p187)) % 0.39/0.68 (step @p190 :rule refl :args (tptp.axidl)) % 0.39/0.68 (step @p191 :rule cong :premises (@p190 @p141) :args (@t25)) % 0.39/0.68 (step @p192 :rule eq_resolve :premises (@p6 @p191)) % 0.39/0.68 (step @p193 :rule not_implies_elim1 :premises (@p117)) % 0.39/0.68 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.39/0.68 (step @p195 :rule refl :args (tptp.axassoc)) % 0.39/0.68 (step @p196 :rule cong :premises (@p195 @p178) :args (@t33)) % 0.39/0.68 (step @p197 :rule eq_resolve :premises (@p8 @p196)) % 0.39/0.68 (step @p198 :rule not_implies_elim1 :premises (@p118)) % 0.39/0.68 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 0.39/0.68 (step @p200 :rule and_intro :premises (@p199 @p194 @p189)) % 0.39/0.68 (step @p201 false :rule contra :premises (@p200 @p184)) % 0.39/0.68 ) % 0.39/0.68 % SZS output end Proof % 0.39/0.68 % cvc5 exiting %------------------------------------------------------------------------------