%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG250^3 : 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 : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:05:38 AM UTC 2026 % Result : Theorem 0.41s 0.73s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ALG250^3 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n005.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 01:54:48 EDT 2026 % 0.17/0.36 % CPUTime : % 0.39/0.58 %----Proving TH0 % 0.41/0.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.73 % SZS status Theorem % 0.41/0.73 % SZS output start Proof % 0.41/0.73 ( % 0.41/0.73 (declare-sort tptp.term 0) % 0.41/0.73 (declare-sort tptp.subst 0) % 0.41/0.73 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.41/0.73 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.41/0.73 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.41/0.73 (declare-const tptp.one tptp.term) % 0.41/0.73 (declare-const tptp.sh tptp.subst) % 0.41/0.73 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.41/0.73 (declare-const tptp.var (-> tptp.term Bool)) % 0.41/0.73 (declare-const tptp.id tptp.subst) % 0.41/0.73 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3b Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3a Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3 Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem2 Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem1 Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasinduction_lem0 Bool) % 0.41/0.73 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasapnotvar Bool) % 0.41/0.73 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.41/0.73 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.41/0.73 (declare-const tptp.hoaslamnotvar Bool) % 0.41/0.73 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.41/0.73 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.41/0.73 (declare-const tptp.hoaslamnotap Bool) % 0.41/0.73 (declare-const tptp.hoaslaminj_lthm Bool) % 0.41/0.73 (declare-const tptp.hoaslaminj_gthm Bool) % 0.41/0.73 (declare-const tptp.hoaslaminj Bool) % 0.41/0.73 (declare-const tptp.hoasapinj2_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasapinj2_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasapinj2 Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.41/0.73 (declare-const tptp.axassoc Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.41/0.73 (declare-const tptp.axvarcons Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem0 Bool) % 0.41/0.73 (declare-const tptp.apinj1 Bool) % 0.41/0.73 (declare-const tptp.induction Bool) % 0.41/0.73 (declare-const tptp.apnotvar Bool) % 0.41/0.73 (declare-const tptp.laminj Bool) % 0.41/0.73 (declare-const tptp.axvarshift Bool) % 0.41/0.73 (declare-const tptp.ulamvarind Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.41/0.73 (declare-const tptp.ulamvarsh Bool) % 0.41/0.73 (declare-const tptp.ulamvar1 Bool) % 0.41/0.73 (declare-const tptp.axabs Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem1 Bool) % 0.41/0.73 (declare-const tptp.shinj Bool) % 0.41/0.73 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.41/0.73 (declare-const tptp.apinj2 Bool) % 0.41/0.73 (declare-const tptp.axvarid Bool) % 0.41/0.73 (declare-const tptp.axidl Bool) % 0.41/0.73 (declare-const tptp.axclos Bool) % 0.41/0.73 (declare-const tptp.termmset Bool) % 0.41/0.73 (declare-const tptp.axshiftcons Bool) % 0.41/0.73 (declare-const tptp.lamnotap Bool) % 0.41/0.73 (declare-const tptp.lamnotvar Bool) % 0.41/0.73 (declare-const tptp.axapp Bool) % 0.41/0.73 (declare-const tptp.axscons Bool) % 0.41/0.73 (declare-const tptp.axmap Bool) % 0.41/0.73 (declare-const tptp.axidr Bool) % 0.41/0.73 (declare-const tptp.induction2lem Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasapinj1_lthm Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem1v2 Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.41/0.73 (declare-const tptp.induction2 Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem2v2 Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem3v2 Bool) % 0.41/0.73 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.41/0.73 (declare-const tptp.pushprop Bool) % 0.41/0.73 (declare-const tptp.pushprop_gthm Bool) % 0.41/0.73 (declare-const tptp.hoasapinj1 Bool) % 0.41/0.73 (declare-const tptp.pushprop_lthm_orig Bool) % 0.41/0.73 (declare-const tptp.pushprop_lthm Bool) % 0.41/0.73 (declare-const tptp.induction2lem_gthm Bool) % 0.41/0.73 (declare-const tptp.induction2lem_lthm Bool) % 0.41/0.73 (declare-const tptp.induction2_gthm Bool) % 0.41/0.73 (declare-const tptp.induction2_lthm Bool) % 0.41/0.73 (declare-const tptp.substmonoid Bool) % 0.41/0.73 (declare-const tptp.substmonoid_gthm Bool) % 0.41/0.73 (declare-const tptp.termmset_gthm Bool) % 0.41/0.73 (declare-const tptp.substmonoid_lthm Bool) % 0.41/0.73 (declare-const tptp.termmset_lthm Bool) % 0.41/0.73 (declare-const tptp.hoasapinj1_gthm Bool) % 0.41/0.73 (define tptp.pushprop_p_and_p_prime () (let ((_let_1 (@var "M" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (let ((_let_3 (@var "X" tptp.term))) (let ((_let_4 (@var "P" (-> tptp.term Bool)))) (let ((_let_5 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_1 _let_4 _let_5) (forall (@list _let_3) (= (_ _let_5 _let_3) (_ _let_4 (_ (_ tptp.sub _let_3) (_ (_ tptp.push _let_2) _let_1)))))))))))) % 0.41/0.73 (define tptp.hoasap () (let ((_let_1 (@var "B" tptp.term))) (let ((_let_2 (@var "N" tptp.subst))) (let ((_let_3 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_3 _let_2 _let_1) (_ (_ tptp.ap (_ (_ tptp.sub _let_3) _let_2)) _let_1)))))) % 0.41/0.73 (define tptp.hoaslam () (let ((_let_1 (@var "F" (-> tptp.subst tptp.term tptp.term)))) (lambda (@list (@var "M" tptp.subst) _let_1) (_ tptp.lam (_ (_ _let_1 tptp.sh) tptp.one))))) % 0.41/0.73 (define tptp.hoasvar () (let ((_let_1 (@var "N" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_2 _let_1) (_ tptp.var (_ (_ tptp.sub _let_2) _let_1)))))) % 0.41/0.73 (define tptp.hoasinduction_p_and_p_prime () (let ((_let_1 (@var "X" tptp.term))) (let ((_let_2 (@var "P" (-> tptp.subst tptp.term tptp.subst Bool)))) (let ((_let_3 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (= (_ _let_3 _let_1) (_ (_ (_ _let_2 tptp.id) _let_1) tptp.id)))))))) % 0.41/0.73 (define @t1 () (@var "M" tptp.subst)) % 0.41/0.73 (define @t2 () (@var "B" tptp.term)) % 0.41/0.73 (define @t3 () (_ tptp.sub @t2)) % 0.41/0.73 (define @t4 () (_ @t3 @t1)) % 0.41/0.73 (define @t5 () (@var "A" tptp.term)) % 0.41/0.73 (define @t6 () (_ tptp.sub @t5)) % 0.41/0.73 (define @t7 () (_ @t6 @t1)) % 0.41/0.73 (define @t8 () (_ tptp.ap @t5)) % 0.41/0.73 (define @t9 () (_ @t8 @t2)) % 0.41/0.73 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.41/0.73 (define @t11 () (_ tptp.sub tptp.one)) % 0.41/0.73 (define @t12 () (@list @t5 @t1)) % 0.41/0.73 (define @t13 () (@list @t5)) % 0.41/0.73 (define @t14 () (forall @t13 (= (_ @t6 tptp.id) @t5))) % 0.41/0.73 (define @t15 () (_ tptp.comp @t1)) % 0.41/0.73 (define @t16 () (_ tptp.push tptp.one)) % 0.41/0.73 (define @t17 () (_ tptp.lam @t5)) % 0.41/0.73 (define @t18 () (@var "N" tptp.subst)) % 0.41/0.73 (define @t19 () (_ @t15 @t18)) % 0.41/0.73 (define @t20 () (@list @t5 @t1 @t18)) % 0.41/0.73 (define @t21 () (forall @t20 (= (_ (_ tptp.sub @t7) @t18) (_ @t6 @t19)))) % 0.41/0.73 (define @t22 () (@list @t1)) % 0.41/0.73 (define @t23 () (forall @t22 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 0.41/0.73 (define @t24 () (_ tptp.comp tptp.sh)) % 0.41/0.73 (define @t25 () (@var "K" tptp.subst)) % 0.41/0.73 (define @t26 () (forall (@list @t1 @t18 @t25) (= (_ (_ tptp.comp @t19) @t25) (_ @t15 (_ (_ tptp.comp @t18) @t25))))) % 0.41/0.73 (define @t27 () (_ @t6 @t18)) % 0.41/0.73 (define @t28 () (_ (_ tptp.push @t27) @t19)) % 0.41/0.73 (define @t29 () (forall @t22 (= (_ @t15 tptp.id) @t1))) % 0.41/0.73 (define @t30 () (_ @t16 tptp.sh)) % 0.41/0.73 (define @t31 () (_ @t6 tptp.sh)) % 0.41/0.73 (define @t32 () (_ tptp.var @t5)) % 0.41/0.73 (define @t33 () (@var "P" (-> tptp.term Bool))) % 0.41/0.73 (define @t34 () (_ @t33 @t5)) % 0.41/0.73 (define @t35 () (forall @t13 (=> @t32 @t34))) % 0.41/0.73 (define @t36 () (@list @t33)) % 0.41/0.73 (define @t37 () (= @t5 @t2)) % 0.41/0.73 (define @t38 () (@var "D" tptp.term)) % 0.41/0.73 (define @t39 () (_ tptp.ap @t2)) % 0.41/0.73 (define @t40 () (@var "C" tptp.term)) % 0.41/0.73 (define @t41 () (= (_ @t8 @t40) (_ @t39 @t38))) % 0.41/0.73 (define @t42 () (@list @t5 @t2 @t40 @t38)) % 0.41/0.73 (define @t43 () (= @t40 @t38)) % 0.41/0.73 (define @t44 () (@list @t5 @t2)) % 0.41/0.73 (define @t45 () (forall @t13 @t34)) % 0.41/0.73 (define @t46 () (_ @t33 @t17)) % 0.41/0.73 (define @t47 () (_ @t33 @t2)) % 0.41/0.73 (define @t48 () (forall @t44 (=> @t34 (=> @t47 (_ @t33 @t9))))) % 0.41/0.73 (define @t49 () (@var "Q" (-> tptp.term Bool))) % 0.41/0.73 (define @t50 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t33) @t49)) % 0.41/0.73 (define @t51 () (@list @t49)) % 0.41/0.73 (define @t52 () (@list @t33 @t5 @t1)) % 0.41/0.73 (define @t53 () (_ tptp.push @t2)) % 0.41/0.73 (define @t54 () (@var "K" (-> tptp.term Bool))) % 0.41/0.73 (define @t55 () (@list @t33 @t49 @t5 @t1)) % 0.41/0.73 (define @t56 () (_ tptp.sub @t40)) % 0.41/0.73 (define @t57 () (@list @t40)) % 0.41/0.73 (define @t58 () (_ tptp.var @t2)) % 0.41/0.73 (define @t59 () (@list @t2)) % 0.41/0.73 (define @t60 () (forall @t59 (=> @t58 (_ @t33 @t4)))) % 0.41/0.73 (define @t61 () (_ @t3 @t10)) % 0.41/0.73 (define @t62 () (_ @t33 @t61)) % 0.41/0.73 (define @t63 () (forall @t59 (=> @t58 @t62))) % 0.41/0.73 (define @t64 () (_ @t49 @t2)) % 0.41/0.73 (define @t65 () (forall @t59 (=> @t58 @t64))) % 0.41/0.73 (define @t66 () (=> @t65 @t63)) % 0.41/0.73 (define @t67 () (=> @t50 @t66)) % 0.41/0.73 (define @t68 () (forall @t55 @t67)) % 0.41/0.73 (define @t69 () (= tptp.pushprop_lem3v2 @t68)) % 0.41/0.73 (define @t70 () (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.41/0.73 (define @t71 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.41/0.73 (define @t72 () (_ @t6 (_ @t53 tptp.id))) % 0.41/0.73 (define @t73 () (forall @t13 (=> (forall @t59 (=> @t47 (_ @t33 @t72))) @t46))) % 0.41/0.73 (define @t74 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.41/0.73 (define @t75 () (=> tptp.induction2lem tptp.induction2)) % 0.41/0.73 (define @t76 () (_ tptp.hoasap tptp.id)) % 0.41/0.73 (define @t77 () (_ (_ @t76 @t5) tptp.id)) % 0.41/0.73 (define @t78 () (= (_ @t77 @t40) (_ (_ (_ @t76 @t2) tptp.id) @t38))) % 0.41/0.73 (define @t79 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.73 (define @t80 () (_ (_ @t79 @t1) @t5)) % 0.41/0.73 (define @t81 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.73 (define @t82 () (_ @t81 @t1)) % 0.41/0.73 (define @t83 () (_ @t82 @t5)) % 0.41/0.73 (define @t84 () (@list @t1 @t5)) % 0.41/0.73 (define @t85 () (_ tptp.hoaslam tptp.id)) % 0.41/0.73 (define @t86 () (_ @t85 (lambda @t84 @t83))) % 0.41/0.73 (define @t87 () (@list @t1 @t5 @t18)) % 0.41/0.73 (define @t88 () (_ (_ @t81 @t19) @t27)) % 0.41/0.73 (define @t89 () (_ (_ tptp.sub @t83) @t18)) % 0.41/0.73 (define @t90 () (forall @t87 (= @t89 @t88))) % 0.41/0.73 (define @t91 () (@list @t81)) % 0.41/0.73 (define @t92 () (_ @t77 @t2)) % 0.41/0.73 (define @t93 () (_ tptp.hoasvar tptp.id)) % 0.41/0.73 (define @t94 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.41/0.73 (define @t95 () (_ (_ tptp.hoasinduction_p_and_p_prime @t94) @t49)) % 0.41/0.73 (define @t96 () (@list @t94)) % 0.41/0.73 (define @t97 () (_ @t49 @t5)) % 0.41/0.73 (define @t98 () (_ @t94 tptp.id)) % 0.41/0.73 (define @t99 () (_ (_ @t98 @t5) tptp.id)) % 0.41/0.73 (define @t100 () (forall @t13 (=> (_ (_ @t93 @t5) tptp.id) @t99))) % 0.41/0.73 (define @t101 () (_ (_ (_ @t94 @t1) @t5) (_ (_ tptp.comp @t25) @t18))) % 0.41/0.73 (define @t102 () (_ (_ (_ @t94 (_ @t15 @t25)) (_ @t6 @t25)) @t18)) % 0.41/0.73 (define @t103 () (@list @t1 @t5 @t18 @t25)) % 0.41/0.73 (define @t104 () (forall @t103 (=> @t102 @t101))) % 0.41/0.73 (define @t105 () (forall @t103 (=> @t101 @t102))) % 0.41/0.73 (define @t106 () (@list @t94 @t49)) % 0.41/0.73 (define @t107 () (_ (_ @t98 @t2) tptp.id)) % 0.41/0.73 (define @t108 () (forall @t44 (=> @t99 (=> @t107 (_ (_ @t98 @t92) tptp.id))))) % 0.41/0.73 (define @t109 () (=> (forall @t13 (=> @t99 (_ (_ @t98 (_ (_ @t81 tptp.id) @t5)) tptp.id))) (_ (_ @t98 @t86) tptp.id))) % 0.41/0.73 (define @t110 () (forall @t91 (=> @t90 @t109))) % 0.41/0.73 (define @t111 () (=> @t110 (=> @t95 (forall @t13 (=> (forall @t59 (=> @t64 (_ @t49 @t72))) (_ @t49 @t17)))))) % 0.41/0.73 (define @t112 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1))))))))))))))))))))))))))))))))))) % 0.41/0.73 (define @t113 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2))))))))))))))))))))))))))))))))))) % 0.41/0.73 (define @t114 () (forall @t59 (=> @t107 (_ (_ @t98 @t72) tptp.id)))) % 0.41/0.73 (define @t115 () (forall @t13 (=> @t114 (_ (_ @t98 (_ tptp.lam (_ @t6 @t30))) tptp.id)))) % 0.41/0.73 (define @t116 () (=> @t110 (forall @t13 (=> @t114 (_ (_ @t98 @t17) tptp.id))))) % 0.41/0.73 (define @t117 () (_ (_ @t81 tptp.sh) tptp.one)) % 0.41/0.73 (define @t118 () (=> @t108 (=> @t110 (forall @t13 @t99)))) % 0.41/0.73 (define @t119 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.41/0.73 (define @t120 () (not tptp.pushprop_lem3v2_lthm)) % 0.41/0.73 (define @t121 () (@var "X" tptp.term)) % 0.41/0.73 (define @t122 () (_ tptp.sub @t121)) % 0.41/0.73 (define @t123 () (_ @t122 @t10)) % 0.41/0.73 (define @t124 () (_ @t33 @t123)) % 0.41/0.73 (define @t125 () (_ @t49 @t121)) % 0.41/0.73 (define @t126 () (= @t125 @t124)) % 0.41/0.73 (define @t127 () (@list @t121)) % 0.41/0.73 (define @t128 () (forall @t127 @t126)) % 0.41/0.73 (define @t129 () (@list @t5 @t1 @t33 @t49)) % 0.41/0.73 (define @t130 () (lambda @t129 @t128)) % 0.41/0.73 (define @t131 () (lambda (@list @t1 @t5 @t18 @t2) (_ (_ tptp.ap @t27) @t2))) % 0.41/0.73 (define @t132 () (lambda (@list @t1 @t81) (_ tptp.lam @t117))) % 0.41/0.73 (define @t133 () (lambda @t87 (_ tptp.var @t27))) % 0.41/0.73 (define @t134 () (lambda @t106 (forall @t127 (= @t125 (_ (_ @t98 @t121) tptp.id))))) % 0.41/0.73 (define @t135 () (tptp.push @t5 @t1)) % 0.41/0.73 (define @t136 () (@var "BOUND_VARIABLE_9302" tptp.term)) % 0.41/0.73 (define @t137 () (_ @t33 (tptp.sub @t136 @t135))) % 0.41/0.73 (define @t138 () (not (tptp.var @t136))) % 0.41/0.73 (define @t139 () (_ @t49 @t2)) % 0.41/0.73 (define @t140 () (tptp.var @t2)) % 0.41/0.73 (define @t141 () (not @t140)) % 0.41/0.73 (define @t142 () (forall @t59 (or @t141 @t139))) % 0.41/0.73 (define @t143 () (not @t142)) % 0.41/0.73 (define @t144 () (tptp.sub @t121 @t135)) % 0.41/0.73 (define @t145 () (_ @t33 @t144)) % 0.41/0.73 (define @t146 () (_ @t49 @t121)) % 0.41/0.73 (define @t147 () (forall @t127 (= @t146 @t145))) % 0.41/0.73 (define @t148 () (not @t147)) % 0.41/0.73 (define @t149 () (or @t148 @t143 @t138 @t137)) % 0.41/0.73 (define @t150 () (or @t138 @t137)) % 0.41/0.73 (define @t151 () (or @t148 @t143 @t150)) % 0.41/0.73 (define @t152 () (@list @t33 @t49 @t5 @t1 @t136)) % 0.41/0.73 (define @t153 () (forall @t152 @t151)) % 0.41/0.73 (define @t154 () (@list @t136)) % 0.41/0.73 (define @t155 () (forall @t154 @t151)) % 0.41/0.73 (define @t156 () (forall @t154 @t150)) % 0.41/0.73 (define @t157 () (or @t148 @t143 @t156)) % 0.41/0.73 (define @t158 () (tptp.sub @t2 @t135)) % 0.41/0.73 (define @t159 () (_ @t33 @t158)) % 0.41/0.73 (define @t160 () (forall @t59 (or @t141 @t159))) % 0.41/0.73 (define @t161 () (or @t148 @t143 @t160)) % 0.41/0.73 (define @t162 () (=> @t142 @t160)) % 0.41/0.73 (define @t163 () (not @t58)) % 0.41/0.73 (define @t164 () (or @t163 @t62)) % 0.41/0.73 (define @t165 () (or @t163 @t64)) % 0.41/0.73 (define @t166 () (lambda @t51 @t147)) % 0.41/0.73 (define @t167 () (lambda (@list @t33 @t49) @t147)) % 0.41/0.73 (define @t168 () (lambda (@list @t1 @t33 @t49) @t147)) % 0.41/0.73 (define @t169 () (_ (lambda @t129 @t147) @t5)) % 0.41/0.73 (define @t170 () (=> (_ (_ (_ @t169 @t1) @t33) @t49) @t66)) % 0.41/0.73 (define @t171 () (forall @t55 @t170)) % 0.41/0.73 (define @t172 () (forall @t152 @t149)) % 0.41/0.73 (define @t173 () (@quantifiers_skolemize @t172 4)) % 0.41/0.73 (define @t174 () (tptp.var @t173)) % 0.41/0.73 (define @t175 () (tptp.push (@quantifiers_skolemize @t172 2) (@quantifiers_skolemize @t172 3))) % 0.41/0.73 (define @t176 () (@quantifiers_skolemize @t172 0)) % 0.41/0.73 (define @t177 () (_ @t176 (tptp.sub @t173 @t175))) % 0.41/0.73 (define @t178 () (not @t174)) % 0.41/0.73 (define @t179 () (@quantifiers_skolemize @t172 1)) % 0.41/0.73 (define @t180 () (forall @t59 (or @t141 (_ @t179 @t2)))) % 0.41/0.73 (define @t181 () (not @t180)) % 0.41/0.73 (define @t182 () (forall @t127 (= (_ @t179 @t121) (_ @t176 (tptp.sub @t121 @t175))))) % 0.41/0.73 (define @t183 () (not @t182)) % 0.41/0.73 (define @t184 () (or @t183 @t181 @t178 @t177)) % 0.41/0.73 (define @t185 () (@list true)) % 0.41/0.73 (define @t186 () (@list @t184)) % 0.41/0.73 (define @t187 () (@list @t173)) % 0.41/0.73 (define @t188 () (_ @t179 @t173)) % 0.41/0.73 (define @t189 () (= @t188 @t177)) % 0.41/0.73 (define @t190 () (= @t177 @t188)) % 0.41/0.73 (define @t191 () (not @t188)) % 0.41/0.73 (define @t192 () (or @t178 @t188)) % 0.41/0.73 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.41/0.73 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.41/0.73 (assume @p3 (= tptp.axvarid @t14)) % 0.41/0.73 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t17) @t1) (_ tptp.lam (_ @t6 (_ @t16 (_ @t15 tptp.sh)))))))) % 0.41/0.73 (assume @p5 (= tptp.axclos @t21)) % 0.41/0.73 (assume @p6 (= tptp.axidl @t23)) % 0.41/0.73 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t24 @t10) @t1)))) % 0.41/0.73 (assume @p8 (= tptp.axassoc @t26)) % 0.41/0.73 (assume @p9 (= tptp.axmap (forall @t20 (= (_ (_ tptp.comp @t10) @t18) @t28)))) % 0.41/0.73 (assume @p10 (= tptp.axidr @t29)) % 0.41/0.73 (assume @p11 (= tptp.axvarshift (= @t30 tptp.id))) % 0.41/0.73 (assume @p12 (= tptp.axscons (forall @t22 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t24 @t1)) @t1)))) % 0.41/0.73 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.41/0.73 (assume @p14 (= tptp.ulamvarsh (forall @t13 (=> @t32 (_ tptp.var @t31))))) % 0.41/0.73 (assume @p15 (= tptp.ulamvarind (forall @t36 (=> (_ @t33 tptp.one) (=> (forall @t13 (=> @t32 (=> @t34 (_ @t33 @t31)))) @t35))))) % 0.41/0.73 (assume @p16 (= tptp.apinj1 (forall @t42 (=> @t41 @t37)))) % 0.41/0.73 (assume @p17 (= tptp.apinj2 (forall @t42 (=> @t41 @t43)))) % 0.41/0.73 (assume @p18 (= tptp.laminj (forall @t44 (=> (= @t17 (_ tptp.lam @t2)) @t37)))) % 0.41/0.73 (assume @p19 (= tptp.shinj (forall @t44 (=> (= @t31 (_ @t3 tptp.sh)) @t37)))) % 0.41/0.73 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t40) (not (= @t17 (_ @t39 @t40)))))) % 0.41/0.73 (assume @p21 (= tptp.apnotvar (forall @t44 (not (_ tptp.var @t9))))) % 0.41/0.73 (assume @p22 (= tptp.lamnotvar (forall @t13 (not (_ tptp.var @t17))))) % 0.41/0.73 (assume @p23 (= tptp.induction (forall @t36 (=> @t35 (=> @t48 (=> (forall @t13 (=> @t34 @t46)) @t45)))))) % 0.41/0.73 (assume @p24 (= tptp.pushprop_lem0 (forall @t52 (exists @t51 @t50)))) % 0.41/0.73 (assume @p25 (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0))))))))))))))))))))))))) % 0.41/0.73 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.41/0.73 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t33 @t54 @t5 @t1 @t2) (=> @t34 (_ @t54 (_ @t6 (_ @t53 @t1))))))) % 0.41/0.73 (assume @p28 (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1))))))))))))))))))))))))) % 0.41/0.73 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.41/0.73 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t55 (=> @t34 (=> @t50 (_ @t49 tptp.one)))))) % 0.41/0.73 (assume @p31 (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2))))))))))))))))))))))))) % 0.41/0.73 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.41/0.73 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t55 (=> @t50 (=> @t60 (forall @t57 (=> (_ tptp.var @t40) (=> (_ @t49 @t40) (_ @t49 (_ @t56 tptp.sh)))))))))) % 0.41/0.73 (assume @p34 (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2))))))))))))))))))))))))) % 0.41/0.73 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.41/0.73 (assume @p36 @t69) % 0.41/0.73 (assume @p37 @t70) % 0.41/0.73 (assume @p38 (= tptp.pushprop (forall @t52 (=> @t60 (=> @t34 @t63))))) % 0.41/0.73 (assume @p39 (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop))))))))))))))))))))))))) % 0.41/0.73 (assume @p40 (= tptp.pushprop_lthm_orig @t71)) % 0.41/0.73 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t71))) % 0.41/0.73 (assume @p42 (= tptp.induction2lem (forall @t36 (=> @t48 (=> @t73 (forall @t12 (=> @t60 (_ @t33 @t7)))))))) % 0.41/0.73 (assume @p43 (= tptp.induction2lem_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar @t74)))))))))))))))))))))))) % 0.41/0.73 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t74)))))))))) % 0.41/0.73 (assume @p45 (= tptp.induction2 (forall @t36 (=> @t35 (=> @t48 (=> @t73 @t45)))))) % 0.41/0.73 (assume @p46 (= tptp.induction2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop @t75)))))))))))))))))))))))))) % 0.41/0.73 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t75))) % 0.41/0.73 (assume @p48 (= tptp.substmonoid (and @t26 @t23 @t29))) % 0.41/0.73 (assume @p49 (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid)))))))))))))))))))))))))))) % 0.41/0.73 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.41/0.73 (assume @p51 (= tptp.termmset (and @t21 @t14))) % 0.41/0.73 (assume @p52 (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.41/0.73 (assume @p54 (= tptp.hoasapinj1 (forall @t42 (=> @t78 @t37)))) % 0.41/0.73 (assume @p55 (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1)))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.41/0.73 (assume @p57 (= tptp.hoasapinj2 (forall @t42 (=> @t78 @t43)))) % 0.41/0.73 (assume @p58 (= tptp.hoasapinj2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 tptp.hoasapinj2))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.41/0.73 (assume @p60 (= tptp.hoaslaminj (forall @t91 (=> @t90 (forall (@list @t79) (=> (forall @t87 (= (_ (_ tptp.sub @t80) @t18) (_ (_ @t79 @t19) @t27))) (=> (= @t86 (_ @t85 (lambda @t84 @t80))) (forall @t84 (= @t83 @t80))))))))) % 0.41/0.73 (assume @p61 (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj)))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.41/0.73 (assume @p63 (= tptp.hoaslamnotap (forall @t91 (=> @t90 (forall @t44 (not (= (_ @t85 (lambda (@list @t1 @t40) (_ @t82 @t40))) @t92))))))) % 0.41/0.73 (assume @p64 (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.41/0.73 (assume @p66 (= tptp.hoaslamnotvar (forall @t91 (=> @t90 (not (_ (_ @t93 @t86) tptp.id)))))) % 0.41/0.73 (assume @p67 (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar)))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.41/0.73 (assume @p69 (= tptp.hoasapnotvar (forall @t44 (not (_ (_ @t93 @t92) tptp.id))))) % 0.41/0.73 (assume @p70 (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.41/0.73 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t96 (exists @t51 @t95)))) % 0.41/0.73 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.41/0.73 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t106 (=> @t105 (=> @t104 (=> @t100 (=> @t95 (forall @t13 (=> @t32 @t97))))))))) % 0.41/0.73 (assume @p75 (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t106 (=> @t105 (=> @t104 (=> @t108 (=> @t95 (forall @t44 (=> @t97 (=> @t64 (_ @t49 @t9))))))))))) % 0.41/0.73 (assume @p77 (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t59 (exists @t91 (forall @t12 (= @t83 @t61)))))) % 0.41/0.73 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.41/0.73 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t106 (=> @t105 (=> @t104 @t111))))) % 0.41/0.73 (assume @p81 (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2)))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.41/0.73 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t106 @t111))) % 0.41/0.73 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.41/0.73 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t96 (=> @t105 (=> @t104 (=> @t100 (forall @t13 (=> @t32 @t99)))))))) % 0.41/0.73 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t112)) % 0.41/0.73 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t112)) % 0.41/0.73 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t96 (=> @t105 (=> @t104 (=> @t108 (forall @t44 (=> @t99 (=> @t107 (_ (_ @t98 @t9) tptp.id)))))))))) % 0.41/0.73 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t113)) % 0.41/0.73 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t113)) % 0.41/0.73 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t96 (=> @t110 @t115)))) % 0.41/0.73 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.41/0.73 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t96 (=> (forall @t91 (=> (exists @t57 (forall @t87 (and (= @t89 (_ (_ tptp.sub (_ @t56 @t10)) @t18)) (= (_ @t56 @t28) @t88)))) @t109)) @t115)))) % 0.41/0.73 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t96 (=> @t105 (=> @t104 @t116))))) % 0.41/0.73 (assume @p95 (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3)))))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.41/0.73 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t96 @t116))) % 0.41/0.73 (assume @p98 (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a)))))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.41/0.73 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t59 (exists @t91 (= (_ @t3 @t30) @t117))))) % 0.41/0.73 (assume @p101 (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b)))))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.41/0.73 (assume @p103 (= tptp.hoasinduction (forall @t96 (=> @t105 (=> @t104 (=> @t100 @t118)))))) % 0.41/0.73 (assume @p104 (= tptp.hoasinduction_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar @t119)))))))))))))))))))))))))))))))))))) % 0.41/0.73 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t119))) % 0.41/0.73 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.41/0.73 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t96 @t118))) % 0.41/0.73 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.41/0.73 (assume @p109 @t120) % 0.41/0.73 (assume @p110 true) % 0.41/0.73 (step @p111 (= tptp.pushprop_p_and_p_prime @t130) :rule refl :args (@t130)) % 0.41/0.73 (step @p112 (= tptp.hoasap @t131) :rule refl :args (@t131)) % 0.41/0.73 (step @p113 (= tptp.hoaslam @t132) :rule refl :args (@t132)) % 0.41/0.73 (step @p114 (= tptp.hoasvar @t133) :rule refl :args (@t133)) % 0.41/0.73 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t134) :rule refl :args (@t134)) % 0.41/0.73 (step @p116 :rule aci_norm :args ((= @t151 @t149))) % 0.41/0.73 (step @p117 :rule cong :premises (@p116) :args (@t153)) % 0.41/0.73 (step @p118 :rule quant-merge-prenex :args ((= (forall @t55 @t155) @t153))) % 0.41/0.73 (step @p119 :rule alpha_equiv :args (@t156 (@list @t136) (@list @t2))) % 0.41/0.73 (step @p120 :rule refl :args (@t143)) % 0.41/0.73 (step @p121 :rule refl :args (@t148)) % 0.41/0.73 (step @p122 :rule nary_cong :premises (@p121 @p120 @p119) :args (@t157)) % 0.41/0.73 (step @p123 :rule quant-miniscope-or :args ((= @t155 @t157))) % 0.41/0.73 (step @p124 :rule trans :premises (@p123 @p122)) % 0.41/0.73 (step @p125 :rule symm :premises (@p124)) % 0.41/0.73 (step @p126 :rule cong :premises (@p125) :args ((forall @t55 @t161))) % 0.41/0.73 (step @p127 :rule trans :premises (@p126 @p118)) % 0.41/0.73 (step @p128 :rule trans :premises (@p127 @p117)) % 0.41/0.73 (step @p129 :rule aci_norm :args ((= (or @t148 (or @t143 @t160)) @t161))) % 0.41/0.73 (step @p130 :rule bool-impl-elim :args (@t142 @t160)) % 0.41/0.73 (step @p131 :rule nary_cong :premises (@p121 @p130) :args ((or @t148 @t162))) % 0.41/0.73 (step @p132 :rule trans :premises (@p131 @p129)) % 0.41/0.73 (step @p133 :rule bool-impl-elim :args (@t147 @t162)) % 0.41/0.73 (step @p134 :rule trans :premises (@p133 @p132)) % 0.41/0.73 (step @p135 :rule cong :premises (@p134) :args ((forall @t55 (=> @t147 @t162)))) % 0.41/0.73 (step @p136 :rule trans :premises (@p135 @p128)) % 0.41/0.73 (step @p137 :rule refl :args ((_ @t33 @t61))) % 0.41/0.73 (step @p138 :rule refl :args ((tptp.sub @t2 @t10))) % 0.41/0.73 (step @p139 :rule refl :args (@t135)) % 0.41/0.73 (step @p140 :rule refl :args (@t2)) % 0.41/0.73 (step @p141 :rule cong :premises (@p140 @p139) :args (@t158)) % 0.41/0.73 (step @p142 :rule trans :premises (@p141 @p138)) % 0.41/0.73 (step @p143 :rule cong :premises (@p142) :args (@t159)) % 0.41/0.73 (step @p144 :rule trans :premises (@p143 @p137)) % 0.41/0.73 (step @p145 :rule refl :args (@t33)) % 0.41/0.73 (step @p146 :rule ho_cong :premises (@p145 @p142)) % 0.41/0.73 (step @p147 :rule cong :premises (@p146 @p144) :args ((= (_ @t33 @t158) @t159))) % 0.41/0.73 (step @p148 :rule symm :premises (@p147)) % 0.41/0.73 (step @p149 :rule refl :args (@t62)) % 0.41/0.73 (step @p150 :rule eq_resolve :premises (@p149 @p148)) % 0.41/0.73 (step @p151 :rule refl :args (@t3)) % 0.41/0.73 (step @p152 :rule ho_cong :premises (@p151 @p139)) % 0.41/0.73 (step @p153 :rule cong :premises (@p152 @p142) :args ((= (_ @t3 @t135) @t158))) % 0.41/0.73 (step @p154 :rule symm :premises (@p153)) % 0.41/0.73 (step @p155 :rule refl :args (@t61)) % 0.41/0.73 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.41/0.73 (step @p157 :rule refl :args (@t10)) % 0.41/0.73 (step @p158 :rule cong :premises (@p157 @p139) :args ((= @t10 @t135))) % 0.41/0.73 (step @p159 :rule symm :premises (@p158)) % 0.41/0.73 (step @p160 :rule eq_resolve :premises (@p157 @p159)) % 0.41/0.73 (step @p161 :rule ho_cong :premises (@p151 @p160)) % 0.41/0.73 (step @p162 :rule trans :premises (@p161 @p156)) % 0.41/0.73 (step @p163 :rule ho_cong :premises (@p145 @p162)) % 0.41/0.73 (step @p164 :rule trans :premises (@p163 @p150)) % 0.41/0.73 (step @p165 :rule refl :args (@t140)) % 0.41/0.73 (step @p166 :rule refl :args (@t58)) % 0.41/0.73 (step @p167 :rule cong :premises (@p166 @p165) :args ((= @t58 @t140))) % 0.41/0.73 (step @p168 :rule symm :premises (@p167)) % 0.41/0.73 (step @p169 :rule eq_resolve :premises (@p166 @p168)) % 0.41/0.73 (step @p170 :rule cong :premises (@p169) :args (@t163)) % 0.41/0.73 (step @p171 :rule nary_cong :premises (@p170 @p164) :args (@t164)) % 0.41/0.73 (step @p172 :rule cong :premises (@p171) :args ((forall @t59 @t164))) % 0.41/0.73 (step @p173 :rule bool-impl-elim :args (@t58 @t62)) % 0.41/0.73 (step @p174 :rule cong :premises (@p173) :args (@t63)) % 0.41/0.73 (step @p175 :rule trans :premises (@p174 @p172)) % 0.41/0.73 (step @p176 :rule refl :args (@t139)) % 0.41/0.73 (step @p177 :rule refl :args (@t64)) % 0.41/0.73 (step @p178 :rule cong :premises (@p177 @p176) :args ((= @t64 @t139))) % 0.41/0.73 (step @p179 :rule symm :premises (@p178)) % 0.41/0.73 (step @p180 :rule eq_resolve :premises (@p177 @p179)) % 0.41/0.73 (step @p181 :rule nary_cong :premises (@p170 @p180) :args (@t165)) % 0.41/0.73 (step @p182 :rule cong :premises (@p181) :args ((forall @t59 @t165))) % 0.41/0.73 (step @p183 :rule bool-impl-elim :args (@t58 @t64)) % 0.41/0.73 (step @p184 :rule cong :premises (@p183) :args (@t65)) % 0.41/0.73 (step @p185 :rule trans :premises (@p184 @p182)) % 0.41/0.73 (step @p186 :rule cong :premises (@p185 @p175) :args (@t66)) % 0.41/0.73 (step @p187 :rule beta-reduce :args ((= (_ @t166 @t49) @t147))) % 0.41/0.73 (step @p188 :rule refl :args (@t49)) % 0.41/0.73 (step @p189 :rule beta-reduce :args ((= (_ @t167 @t33) @t166))) % 0.41/0.73 (step @p190 :rule refl :args (@t33)) % 0.41/0.73 (step @p191 :rule beta-reduce :args ((= (_ @t168 @t1) @t167))) % 0.41/0.73 (step @p192 :rule refl :args (@t1)) % 0.41/0.73 (step @p193 :rule beta-reduce :args ((= @t169 @t168))) % 0.41/0.73 (step @p194 :rule ho_cong :premises (@p193 @p192)) % 0.41/0.73 (step @p195 :rule trans :premises (@p194 @p191)) % 0.41/0.73 (step @p196 :rule ho_cong :premises (@p195 @p190)) % 0.41/0.73 (step @p197 :rule trans :premises (@p196 @p189)) % 0.41/0.73 (step @p198 :rule ho_cong :premises (@p197 @p188)) % 0.41/0.73 (step @p199 :rule trans :premises (@p198 @p187)) % 0.41/0.73 (step @p200 :rule cong :premises (@p199 @p186) :args (@t170)) % 0.41/0.73 (step @p201 :rule cong :premises (@p200) :args (@t171)) % 0.41/0.73 (step @p202 :rule trans :premises (@p201 @p136)) % 0.41/0.73 (step @p203 :rule refl :args (tptp.pushprop_lem3v2)) % 0.41/0.73 (step @p204 :rule cong :premises (@p203 @p202) :args ((= tptp.pushprop_lem3v2 @t171))) % 0.41/0.73 (step @p205 :rule refl :args (@t66)) % 0.41/0.73 (step @p206 :rule refl :args (@t5)) % 0.41/0.73 (step @p207 :rule refl :args ((_ @t33 @t123))) % 0.41/0.73 (step @p208 :rule refl :args ((tptp.sub @t121 @t10))) % 0.41/0.73 (step @p209 :rule refl :args (@t121)) % 0.41/0.73 (step @p210 :rule cong :premises (@p209 @p139) :args (@t144)) % 0.41/0.73 (step @p211 :rule trans :premises (@p210 @p208)) % 0.41/0.73 (step @p212 :rule cong :premises (@p211) :args (@t145)) % 0.41/0.73 (step @p213 :rule trans :premises (@p212 @p207)) % 0.41/0.73 (step @p214 :rule ho_cong :premises (@p145 @p211)) % 0.41/0.73 (step @p215 :rule cong :premises (@p214 @p213) :args ((= (_ @t33 @t144) @t145))) % 0.41/0.73 (step @p216 :rule symm :premises (@p215)) % 0.41/0.73 (step @p217 :rule refl :args (@t124)) % 0.41/0.73 (step @p218 :rule eq_resolve :premises (@p217 @p216)) % 0.41/0.73 (step @p219 :rule refl :args (@t122)) % 0.41/0.73 (step @p220 :rule ho_cong :premises (@p219 @p139)) % 0.41/0.73 (step @p221 :rule cong :premises (@p220 @p211) :args ((= (_ @t122 @t135) @t144))) % 0.41/0.73 (step @p222 :rule symm :premises (@p221)) % 0.41/0.73 (step @p223 :rule refl :args (@t123)) % 0.41/0.73 (step @p224 :rule eq_resolve :premises (@p223 @p222)) % 0.41/0.73 (step @p225 :rule ho_cong :premises (@p219 @p160)) % 0.41/0.73 (step @p226 :rule trans :premises (@p225 @p224)) % 0.41/0.73 (step @p227 :rule ho_cong :premises (@p145 @p226)) % 0.41/0.73 (step @p228 :rule trans :premises (@p227 @p218)) % 0.41/0.73 (step @p229 :rule refl :args (@t146)) % 0.41/0.73 (step @p230 :rule refl :args (@t125)) % 0.41/0.73 (step @p231 :rule cong :premises (@p230 @p229) :args ((= @t125 @t146))) % 0.41/0.73 (step @p232 :rule symm :premises (@p231)) % 0.41/0.73 (step @p233 :rule eq_resolve :premises (@p230 @p232)) % 0.41/0.73 (step @p234 :rule cong :premises (@p233 @p228) :args (@t126)) % 0.41/0.73 (step @p235 :rule cong :premises (@p234) :args (@t128)) % 0.41/0.73 (step @p236 :rule cong :premises (@p235) :args (@t130)) % 0.41/0.73 (step @p237 :rule trans :premises (@p111 @p236)) % 0.41/0.73 (step @p238 :rule ho_cong :premises (@p237 @p206)) % 0.41/0.73 (step @p239 :rule ho_cong :premises (@p238 @p192)) % 0.41/0.73 (step @p240 :rule ho_cong :premises (@p239 @p190)) % 0.41/0.73 (step @p241 :rule ho_cong :premises (@p240 @p188)) % 0.41/0.73 (step @p242 :rule cong :premises (@p241 @p205) :args (@t67)) % 0.41/0.73 (step @p243 :rule cong :premises (@p242) :args (@t68)) % 0.41/0.73 (step @p244 :rule cong :premises (@p203 @p243) :args (@t69)) % 0.41/0.73 (step @p245 :rule trans :premises (@p244 @p204)) % 0.41/0.73 (step @p246 :rule eq_resolve :premises (@p36 @p245)) % 0.41/0.73 (step @p247 :rule refl :args (tptp.pushprop_lem3v2_lthm)) % 0.41/0.73 (step @p248 :rule cong :premises (@p247 @p246) :args (@t70)) % 0.41/0.73 (step @p249 :rule eq_resolve :premises (@p37 @p248)) % 0.41/0.73 (step @p250 :rule cong :premises (@p249) :args (@t120)) % 0.41/0.73 (step @p251 :rule eq_resolve :premises (@p109 @p250)) % 0.41/0.73 (step @p252 :rule skolemize :premises (@p251)) % 0.41/0.73 (step @p253 :rule bool-double-not-elim :args (@t174)) % 0.41/0.73 (step @p254 :rule refl :args (@t184)) % 0.41/0.73 (step @p255 :rule nary_cong :premises (@p254 @p253) :args ((or @t184 (not @t178)))) % 0.41/0.73 (step @p256 :rule cnf_or_neg :args (@t184 2)) % 0.41/0.73 (step @p257 :rule eq_resolve :premises (@p256 @p255)) % 0.41/0.73 (step @p258 :rule reordering :premises (@p257) :args ((or @t174 @t184))) % 0.41/0.73 (step @p259 :rule chain_m_resolution :premises (@p258 @p252) :args (@t174 @t185 @t186)) % 0.41/0.73 (step @p260 :rule bool-double-not-elim :args (@t180)) % 0.41/0.73 (step @p261 :rule nary_cong :premises (@p254 @p260) :args ((or @t184 (not @t181)))) % 0.41/0.73 (step @p262 :rule cnf_or_neg :args (@t184 1)) % 0.41/0.73 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.41/0.73 (step @p264 :rule reordering :premises (@p263) :args ((or @t180 @t184))) % 0.41/0.73 (step @p265 :rule chain_m_resolution :premises (@p264 @p252) :args (@t180 @t185 @t186)) % 0.41/0.73 (step @p266 :rule instantiate :premises (@p265) :args (@t187)) % 0.41/0.73 (step @p267 :rule bool-double-not-elim :args (@t182)) % 0.41/0.73 (step @p268 :rule nary_cong :premises (@p254 @p267) :args ((or @t184 (not @t183)))) % 0.41/0.73 (step @p269 :rule cnf_or_neg :args (@t184 0)) % 0.41/0.73 (step @p270 :rule eq_resolve :premises (@p269 @p268)) % 0.41/0.73 (step @p271 :rule reordering :premises (@p270) :args ((or @t182 @t184))) % 0.41/0.73 (step @p272 :rule chain_m_resolution :premises (@p271 @p252) :args (@t182 @t185 @t186)) % 0.41/0.73 (step @p273 :rule eq-symm :args (@t188 @t177)) % 0.41/0.73 (step @p274 :rule refl :args (@t182)) % 0.41/0.73 (step @p275 :rule cong :premises (@p274 @p273) :args ((=> @t182 @t189))) % 0.41/0.73 (assume-push @p291 @t182) % 0.41/0.73 (step @p277 :rule instantiate :premises (@p272) :args (@t187)) % 0.41/0.73 (step-pop @p292 :rule scope :premises (@p277)) % 0.41/0.73 (step @p278 :rule process_scope :premises (@p292) :args (@t189)) % 0.41/0.73 (step @p280 :rule eq_resolve :premises (@p278 @p275)) % 0.41/0.73 (step @p281 :rule implies_elim :premises (@p280)) % 0.41/0.73 (step @p282 :rule chain_m_resolution :premises (@p281 @p272) :args (@t190 (@list false) (@list @t182))) % 0.41/0.73 (step @p283 :rule cnf_or_neg :args (@t184 3)) % 0.41/0.73 (step @p284 :rule chain_m_resolution :premises (@p283 @p252) :args ((not @t177) @t185 @t186)) % 0.41/0.73 (step @p285 :rule cnf_equiv_pos2 :args (@t190)) % 0.41/0.73 (step @p286 :rule reordering :premises (@p285) :args ((or @t177 @t191 (not @t190)))) % 0.41/0.73 (step @p287 :rule chain_m_resolution :premises (@p286 @p284 @p282) :args (@t191 (@list true false) (@list @t177 @t190))) % 0.41/0.73 (step @p288 :rule cnf_or_pos :args (@t192)) % 0.41/0.73 (step @p289 :rule reordering :premises (@p288) :args ((or @t178 @t188 (not @t192)))) % 0.41/0.73 (step @p290 false :rule chain_m_resolution :premises (@p289 @p287 @p266 @p259) :args (false (@list true false false) (@list @t188 @t192 @t174))) % 0.41/0.73 ) % 0.41/0.73 % SZS output end Proof % 0.41/0.73 % cvc5 exiting %------------------------------------------------------------------------------