%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG266^2 : 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 : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:05:42 AM UTC 2026 % Result : Theorem 1.12s 1.30s % Output : Proof 1.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG266^2 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n018.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 01:55:20 EDT 2026 % 0.17/0.35 % CPUTime : % 0.39/0.56 %----Proving TH0 % 1.12/1.30 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.12/1.30 % SZS status Theorem % 1.12/1.30 % SZS output start Proof % 1.12/1.30 ( % 1.12/1.30 (declare-sort tptp.term 0) % 1.12/1.30 (declare-sort tptp.subst 0) % 1.12/1.30 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 1.12/1.30 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 1.12/1.30 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 1.12/1.30 (declare-const tptp.one tptp.term) % 1.12/1.30 (declare-const tptp.sh tptp.subst) % 1.12/1.30 (declare-const tptp.lam (-> tptp.term tptp.term)) % 1.12/1.30 (declare-const tptp.var (-> tptp.term Bool)) % 1.12/1.30 (declare-const tptp.id tptp.subst) % 1.12/1.30 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lthm_3 Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3b Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3a Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3 Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3aaa Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3aa Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem2 Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem1 Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3v2a Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3v2 Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem2v2 Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem1v2 Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasinduction_lem0 Bool) % 1.12/1.30 (declare-const tptp.hoasapnotvar_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasapnotvar_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasapnotvar Bool) % 1.12/1.30 (declare-const tptp.hoaslamnotvar_lthm Bool) % 1.12/1.30 (declare-const tptp.hoaslamnotvar_gthm Bool) % 1.12/1.30 (declare-const tptp.hoaslamnotvar Bool) % 1.12/1.30 (declare-const tptp.hoaslamnotap_lthm Bool) % 1.12/1.30 (declare-const tptp.hoaslamnotap_gthm Bool) % 1.12/1.30 (declare-const tptp.hoaslamnotap Bool) % 1.12/1.30 (declare-const tptp.hoaslaminj_lthm Bool) % 1.12/1.30 (declare-const tptp.hoaslaminj_gthm Bool) % 1.12/1.30 (declare-const tptp.hoaslaminj Bool) % 1.12/1.30 (declare-const tptp.hoasapinj2_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasapinj2_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasapinj2 Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem0_lthm Bool) % 1.12/1.30 (declare-const tptp.axassoc Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem0_gthm Bool) % 1.12/1.30 (declare-const tptp.axvarcons Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem0 Bool) % 1.12/1.30 (declare-const tptp.apinj1 Bool) % 1.12/1.30 (declare-const tptp.induction Bool) % 1.12/1.30 (declare-const tptp.apnotvar Bool) % 1.12/1.30 (declare-const tptp.laminj Bool) % 1.12/1.30 (declare-const tptp.axvarshift Bool) % 1.12/1.30 (declare-const tptp.ulamvarind Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 1.12/1.30 (declare-const tptp.ulamvarsh Bool) % 1.12/1.30 (declare-const tptp.ulamvar1 Bool) % 1.12/1.30 (declare-const tptp.axabs Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem1 Bool) % 1.12/1.30 (declare-const tptp.shinj Bool) % 1.12/1.30 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 1.12/1.30 (declare-const tptp.apinj2 Bool) % 1.12/1.30 (declare-const tptp.axvarid Bool) % 1.12/1.30 (declare-const tptp.axidl Bool) % 1.12/1.30 (declare-const tptp.axclos Bool) % 1.12/1.30 (declare-const tptp.termmset Bool) % 1.12/1.30 (declare-const tptp.axshiftcons Bool) % 1.12/1.30 (declare-const tptp.lamnotap Bool) % 1.12/1.30 (declare-const tptp.lamnotvar Bool) % 1.12/1.30 (declare-const tptp.axapp Bool) % 1.12/1.30 (declare-const tptp.axscons Bool) % 1.12/1.30 (declare-const tptp.axmap Bool) % 1.12/1.30 (declare-const tptp.axidr Bool) % 1.12/1.30 (declare-const tptp.induction2lem Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem1_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasapinj1_lthm Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem1_lthm Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem1v2 Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 1.12/1.30 (declare-const tptp.induction2 Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem2v2 Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem3v2 Bool) % 1.12/1.30 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 1.12/1.30 (declare-const tptp.pushprop Bool) % 1.12/1.30 (declare-const tptp.pushprop_gthm Bool) % 1.12/1.30 (declare-const tptp.hoasapinj1 Bool) % 1.12/1.30 (declare-const tptp.pushprop_lthm_orig Bool) % 1.12/1.30 (declare-const tptp.pushprop_lthm Bool) % 1.12/1.30 (declare-const tptp.induction2lem_gthm Bool) % 1.12/1.30 (declare-const tptp.induction2lem_lthm Bool) % 1.12/1.30 (declare-const tptp.induction2_gthm Bool) % 1.12/1.30 (declare-const tptp.induction2_lthm Bool) % 1.12/1.30 (declare-const tptp.substmonoid Bool) % 1.12/1.30 (declare-const tptp.substmonoid_gthm Bool) % 1.12/1.30 (declare-const tptp.termmset_gthm Bool) % 1.12/1.30 (declare-const tptp.substmonoid_lthm Bool) % 1.12/1.30 (declare-const tptp.termmset_lthm Bool) % 1.12/1.30 (declare-const tptp.hoasapinj1_gthm Bool) % 1.12/1.30 (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)))))))))))) % 1.12/1.30 (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)))))) % 1.12/1.30 (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))))) % 1.12/1.30 (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)))))) % 1.12/1.30 (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)))))))) % 1.12/1.30 (define @t1 () (@var "M" tptp.subst)) % 1.12/1.30 (define @t2 () (@var "B" tptp.term)) % 1.12/1.30 (define @t3 () (_ tptp.sub @t2)) % 1.12/1.30 (define @t4 () (_ @t3 @t1)) % 1.12/1.30 (define @t5 () (@var "A" tptp.term)) % 1.12/1.30 (define @t6 () (_ tptp.sub @t5)) % 1.12/1.30 (define @t7 () (_ @t6 @t1)) % 1.12/1.30 (define @t8 () (_ tptp.ap @t5)) % 1.12/1.30 (define @t9 () (_ @t8 @t2)) % 1.12/1.30 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 1.12/1.30 (define @t11 () (_ tptp.sub tptp.one)) % 1.12/1.30 (define @t12 () (@list @t5 @t1)) % 1.12/1.30 (define @t13 () (_ @t6 tptp.id)) % 1.12/1.30 (define @t14 () (@list @t5)) % 1.12/1.30 (define @t15 () (forall @t14 (= @t13 @t5))) % 1.12/1.30 (define @t16 () (= tptp.axvarid @t15)) % 1.12/1.30 (define @t17 () (_ tptp.comp @t1)) % 1.12/1.30 (define @t18 () (_ tptp.push tptp.one)) % 1.12/1.30 (define @t19 () (_ tptp.lam @t5)) % 1.12/1.30 (define @t20 () (@var "N" tptp.subst)) % 1.12/1.30 (define @t21 () (_ @t17 @t20)) % 1.12/1.30 (define @t22 () (@list @t5 @t1 @t20)) % 1.12/1.30 (define @t23 () (forall @t22 (= (_ (_ tptp.sub @t7) @t20) (_ @t6 @t21)))) % 1.12/1.30 (define @t24 () (@list @t1)) % 1.12/1.30 (define @t25 () (forall @t24 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 1.12/1.30 (define @t26 () (_ tptp.comp tptp.sh)) % 1.12/1.30 (define @t27 () (@var "K" tptp.subst)) % 1.12/1.30 (define @t28 () (forall (@list @t1 @t20 @t27) (= (_ (_ tptp.comp @t21) @t27) (_ @t17 (_ (_ tptp.comp @t20) @t27))))) % 1.12/1.30 (define @t29 () (_ @t6 @t20)) % 1.12/1.30 (define @t30 () (_ (_ tptp.push @t29) @t21)) % 1.12/1.30 (define @t31 () (forall @t24 (= (_ @t17 tptp.id) @t1))) % 1.12/1.30 (define @t32 () (_ @t18 tptp.sh)) % 1.12/1.30 (define @t33 () (= tptp.axvarshift (= @t32 tptp.id))) % 1.12/1.30 (define @t34 () (_ @t6 tptp.sh)) % 1.12/1.30 (define @t35 () (_ tptp.var @t5)) % 1.12/1.30 (define @t36 () (@var "P" (-> tptp.term Bool))) % 1.12/1.30 (define @t37 () (_ @t36 @t5)) % 1.12/1.30 (define @t38 () (forall @t14 (=> @t35 @t37))) % 1.12/1.30 (define @t39 () (@list @t36)) % 1.12/1.30 (define @t40 () (= @t5 @t2)) % 1.12/1.30 (define @t41 () (@var "D" tptp.term)) % 1.12/1.30 (define @t42 () (_ tptp.ap @t2)) % 1.12/1.30 (define @t43 () (@var "C" tptp.term)) % 1.12/1.30 (define @t44 () (= (_ @t8 @t43) (_ @t42 @t41))) % 1.12/1.30 (define @t45 () (@list @t5 @t2 @t43 @t41)) % 1.12/1.30 (define @t46 () (= @t43 @t41)) % 1.12/1.30 (define @t47 () (@list @t5 @t2)) % 1.12/1.30 (define @t48 () (forall @t14 @t37)) % 1.12/1.30 (define @t49 () (_ @t36 @t19)) % 1.12/1.30 (define @t50 () (_ @t36 @t2)) % 1.12/1.30 (define @t51 () (forall @t47 (=> @t37 (=> @t50 (_ @t36 @t9))))) % 1.12/1.30 (define @t52 () (@var "Q" (-> tptp.term Bool))) % 1.12/1.30 (define @t53 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t36) @t52)) % 1.12/1.30 (define @t54 () (@list @t52)) % 1.12/1.30 (define @t55 () (@list @t36 @t5 @t1)) % 1.12/1.30 (define @t56 () (_ tptp.push @t2)) % 1.12/1.30 (define @t57 () (@var "K" (-> tptp.term Bool))) % 1.12/1.30 (define @t58 () (@list @t36 @t52 @t5 @t1)) % 1.12/1.30 (define @t59 () (_ tptp.sub @t43)) % 1.12/1.30 (define @t60 () (@list @t43)) % 1.12/1.30 (define @t61 () (_ tptp.var @t2)) % 1.12/1.30 (define @t62 () (@list @t2)) % 1.12/1.30 (define @t63 () (forall @t62 (=> @t61 (_ @t36 @t4)))) % 1.12/1.30 (define @t64 () (_ @t3 @t10)) % 1.12/1.30 (define @t65 () (forall @t62 (=> @t61 (_ @t36 @t64)))) % 1.12/1.30 (define @t66 () (_ @t52 @t2)) % 1.12/1.30 (define @t67 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 1.12/1.30 (define @t68 () (_ @t56 tptp.id)) % 1.12/1.30 (define @t69 () (_ @t6 @t68)) % 1.12/1.30 (define @t70 () (forall @t14 (=> (forall @t62 (=> @t50 (_ @t36 @t69))) @t49))) % 1.12/1.30 (define @t71 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 1.12/1.30 (define @t72 () (=> tptp.induction2lem tptp.induction2)) % 1.12/1.30 (define @t73 () (_ tptp.hoasap tptp.id)) % 1.12/1.30 (define @t74 () (_ (_ @t73 @t5) tptp.id)) % 1.12/1.30 (define @t75 () (= (_ @t74 @t43) (_ (_ (_ @t73 @t2) tptp.id) @t41))) % 1.12/1.30 (define @t76 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 1.12/1.30 (define @t77 () (_ (_ @t76 @t1) @t5)) % 1.12/1.30 (define @t78 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 1.12/1.30 (define @t79 () (_ @t78 @t1)) % 1.12/1.30 (define @t80 () (_ @t79 @t5)) % 1.12/1.30 (define @t81 () (@list @t1 @t5)) % 1.12/1.30 (define @t82 () (_ tptp.hoaslam tptp.id)) % 1.12/1.30 (define @t83 () (lambda @t81 @t80)) % 1.12/1.30 (define @t84 () (_ @t82 @t83)) % 1.12/1.30 (define @t85 () (@list @t1 @t5 @t20)) % 1.12/1.30 (define @t86 () (_ (_ @t78 @t21) @t29)) % 1.12/1.30 (define @t87 () (_ (_ tptp.sub @t80) @t20)) % 1.12/1.30 (define @t88 () (= @t87 @t86)) % 1.12/1.30 (define @t89 () (forall @t85 @t88)) % 1.12/1.30 (define @t90 () (@list @t78)) % 1.12/1.30 (define @t91 () (_ @t74 @t2)) % 1.12/1.30 (define @t92 () (_ tptp.hoasvar tptp.id)) % 1.12/1.30 (define @t93 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 1.12/1.30 (define @t94 () (_ (_ tptp.hoasinduction_p_and_p_prime @t93) @t52)) % 1.12/1.30 (define @t95 () (@list @t93)) % 1.12/1.30 (define @t96 () (_ @t52 @t5)) % 1.12/1.30 (define @t97 () (_ @t93 tptp.id)) % 1.12/1.30 (define @t98 () (_ (_ @t97 @t5) tptp.id)) % 1.12/1.30 (define @t99 () (forall @t14 (=> (_ (_ @t92 @t5) tptp.id) @t98))) % 1.12/1.30 (define @t100 () (_ (_ (_ @t93 @t1) @t5) (_ (_ tptp.comp @t27) @t20))) % 1.12/1.30 (define @t101 () (_ (_ (_ @t93 (_ @t17 @t27)) (_ @t6 @t27)) @t20)) % 1.12/1.30 (define @t102 () (@list @t1 @t5 @t20 @t27)) % 1.12/1.30 (define @t103 () (forall @t102 (=> @t101 @t100))) % 1.12/1.30 (define @t104 () (forall @t102 (=> @t100 @t101))) % 1.12/1.30 (define @t105 () (@list @t93 @t52)) % 1.12/1.30 (define @t106 () (_ (_ @t97 @t2) tptp.id)) % 1.12/1.30 (define @t107 () (forall @t47 (=> @t98 (=> @t106 (_ (_ @t97 @t91) tptp.id))))) % 1.12/1.30 (define @t108 () (_ (_ @t78 tptp.id) @t5)) % 1.12/1.30 (define @t109 () (_ (_ @t97 @t108) tptp.id)) % 1.12/1.30 (define @t110 () (forall @t14 (=> @t98 @t109))) % 1.12/1.30 (define @t111 () (=> @t110 (_ (_ @t97 @t84) tptp.id))) % 1.12/1.30 (define @t112 () (=> @t89 @t111)) % 1.12/1.30 (define @t113 () (forall @t90 @t112)) % 1.12/1.30 (define @t114 () (=> @t113 (=> @t94 (forall @t14 (=> (forall @t62 (=> @t66 (_ @t52 @t69))) (_ @t52 @t19)))))) % 1.12/1.30 (define @t115 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1))))))))))))))))))))))))))))))))))) % 1.12/1.30 (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_lem2))))))))))))))))))))))))))))))))))) % 1.12/1.30 (define @t117 () (_ @t6 @t32)) % 1.12/1.30 (define @t118 () (_ tptp.lam @t117)) % 1.12/1.30 (define @t119 () (_ (_ @t97 @t118) tptp.id)) % 1.12/1.30 (define @t120 () (_ (_ @t97 @t69) tptp.id)) % 1.12/1.30 (define @t121 () (forall @t62 (=> @t106 @t120))) % 1.12/1.30 (define @t122 () (=> @t121 @t119)) % 1.12/1.30 (define @t123 () (forall @t14 @t122)) % 1.12/1.30 (define @t124 () (=> @t113 @t123)) % 1.12/1.30 (define @t125 () (forall @t95 @t124)) % 1.12/1.30 (define @t126 () (= tptp.hoasinduction_lem3aa @t125)) % 1.12/1.30 (define @t127 () (_ (_ @t97 @t19) tptp.id)) % 1.12/1.30 (define @t128 () (=> @t121 @t127)) % 1.12/1.30 (define @t129 () (forall @t14 @t128)) % 1.12/1.30 (define @t130 () (=> @t113 @t129)) % 1.12/1.30 (define @t131 () (forall @t95 @t130)) % 1.12/1.30 (define @t132 () (= tptp.hoasinduction_lem3a @t131)) % 1.12/1.30 (define @t133 () (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a)) % 1.12/1.30 (define @t134 () (=> tptp.axvarshift @t133)) % 1.12/1.30 (define @t135 () (=> tptp.axvarid @t134)) % 1.12/1.30 (define @t136 () (= tptp.hoasinduction_lem3a_lthm @t135)) % 1.12/1.30 (define @t137 () (_ @t78 tptp.sh)) % 1.12/1.30 (define @t138 () (_ @t137 tptp.one)) % 1.12/1.30 (define @t139 () (=> @t107 (=> @t113 (forall @t14 @t98)))) % 1.12/1.30 (define @t140 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 1.12/1.30 (define @t141 () (not tptp.hoasinduction_lem3a_lthm)) % 1.12/1.30 (define @t142 () (@var "X" tptp.term)) % 1.12/1.30 (define @t143 () (_ @t52 @t142)) % 1.12/1.30 (define @t144 () (@list @t142)) % 1.12/1.30 (define @t145 () (lambda (@list @t5 @t1 @t36 @t52) (forall @t144 (= @t143 (_ @t36 (_ (_ tptp.sub @t142) @t10)))))) % 1.12/1.30 (define @t146 () (lambda (@list @t1 @t5 @t20 @t2) (_ (_ tptp.ap @t29) @t2))) % 1.12/1.30 (define @t147 () (_ tptp.lam @t138)) % 1.12/1.30 (define @t148 () (lambda (@list @t1 @t78) @t147)) % 1.12/1.30 (define @t149 () (lambda @t85 (_ tptp.var @t29))) % 1.12/1.30 (define @t150 () (lambda @t105 (forall @t144 (= @t143 (_ (_ @t97 @t142) tptp.id))))) % 1.12/1.30 (define @t151 () (tptp.push tptp.one tptp.sh)) % 1.12/1.30 (define @t152 () (@var "BOUND_VARIABLE_10260" tptp.term)) % 1.12/1.30 (define @t153 () (tptp.lam @t152)) % 1.12/1.30 (define @t154 () (tptp.push @t2 @t151)) % 1.12/1.30 (define @t155 () (not (_ @t93 @t151 @t2 @t151))) % 1.12/1.30 (define @t156 () (not (forall @t62 (or @t155 (_ @t93 @t151 (tptp.sub @t152 @t154) @t151))))) % 1.12/1.30 (define @t157 () (_ @t78 tptp.sh tptp.one)) % 1.12/1.30 (define @t158 () (tptp.lam @t157)) % 1.12/1.30 (define @t159 () (_ @t78 @t151 @t5)) % 1.12/1.30 (define @t160 () (not (forall @t14 (or (not (_ @t93 @t151 @t5 @t151)) (_ @t93 @t151 @t159 @t151))))) % 1.12/1.30 (define @t161 () (tptp.sub @t5 @t20)) % 1.12/1.30 (define @t162 () (tptp.comp @t1 @t20)) % 1.12/1.30 (define @t163 () (_ @t78 @t162 @t161)) % 1.12/1.30 (define @t164 () (_ @t78 @t1 @t5)) % 1.12/1.30 (define @t165 () (tptp.sub @t164 @t20)) % 1.12/1.30 (define @t166 () (forall @t85 (= @t165 @t163))) % 1.12/1.30 (define @t167 () (not @t166)) % 1.12/1.30 (define @t168 () (not (forall @t90 (or @t167 @t160 (_ @t93 @t151 @t158 @t151))))) % 1.12/1.30 (define @t169 () (@list @t93 @t152)) % 1.12/1.30 (define @t170 () (forall @t169 (or @t168 @t156 (_ @t93 @t151 @t153 @t151)))) % 1.12/1.30 (define @t171 () (@var "BOUND_VARIABLE_10074" tptp.term)) % 1.12/1.30 (define @t172 () (tptp.lam (tptp.sub @t171 @t151))) % 1.12/1.30 (define @t173 () (not (forall @t62 (or @t155 (_ @t93 @t151 (tptp.sub @t171 @t154) @t151))))) % 1.12/1.30 (define @t174 () (@list @t93 @t171)) % 1.12/1.30 (define @t175 () (forall @t174 (or @t168 @t173 (_ @t93 @t151 @t172 @t151)))) % 1.12/1.30 (define @t176 () (_ @t93 @t32 @t153 @t32)) % 1.12/1.30 (define @t177 () (or @t168 @t156 @t176)) % 1.12/1.30 (define @t178 () (tptp.push @t2 @t32)) % 1.12/1.30 (define @t179 () (tptp.sub @t152 @t178)) % 1.12/1.30 (define @t180 () (_ @t93 @t32 @t179 @t32)) % 1.12/1.30 (define @t181 () (_ @t93 @t32 @t2 @t32)) % 1.12/1.30 (define @t182 () (not @t181)) % 1.12/1.30 (define @t183 () (or @t182 @t180)) % 1.12/1.30 (define @t184 () (forall @t62 @t183)) % 1.12/1.30 (define @t185 () (not @t184)) % 1.12/1.30 (define @t186 () (_ @t93 @t32 @t158 @t32)) % 1.12/1.30 (define @t187 () (or @t167 @t160 @t186)) % 1.12/1.30 (define @t188 () (_ @t78 @t32 @t5)) % 1.12/1.30 (define @t189 () (_ @t93 @t32 @t188 @t32)) % 1.12/1.30 (define @t190 () (_ @t93 @t32 @t5 @t32)) % 1.12/1.30 (define @t191 () (not @t190)) % 1.12/1.30 (define @t192 () (or @t191 @t189)) % 1.12/1.30 (define @t193 () (forall @t14 @t192)) % 1.12/1.30 (define @t194 () (not @t193)) % 1.12/1.30 (define @t195 () (or @t167 @t194 @t186)) % 1.12/1.30 (define @t196 () (forall @t90 @t195)) % 1.12/1.30 (define @t197 () (not @t196)) % 1.12/1.30 (define @t198 () (or @t197 @t185 @t176)) % 1.12/1.30 (define @t199 () (forall @t169 @t198)) % 1.12/1.30 (define @t200 () (_ @t93 @t32 @t172 @t32)) % 1.12/1.30 (define @t201 () (or @t168 @t173 @t200)) % 1.12/1.30 (define @t202 () (tptp.sub @t171 @t178)) % 1.12/1.30 (define @t203 () (_ @t93 @t32 @t202 @t32)) % 1.12/1.30 (define @t204 () (or @t182 @t203)) % 1.12/1.30 (define @t205 () (forall @t62 @t204)) % 1.12/1.30 (define @t206 () (not @t205)) % 1.12/1.30 (define @t207 () (or @t197 @t206 @t200)) % 1.12/1.30 (define @t208 () (forall @t174 @t207)) % 1.12/1.30 (define @t209 () (=> @t208 @t199)) % 1.12/1.30 (define @t210 () (=> (= @t32 @t32) @t209)) % 1.12/1.30 (define @t211 () (tptp.sub @t5 @t32)) % 1.12/1.30 (define @t212 () (= @t5 @t211)) % 1.12/1.30 (define @t213 () (forall @t14 @t212)) % 1.12/1.30 (define @t214 () (=> @t213 @t210)) % 1.12/1.30 (define @t215 () (_ @t93 tptp.id @t153 tptp.id)) % 1.12/1.30 (define @t216 () (tptp.push @t2 tptp.id)) % 1.12/1.30 (define @t217 () (tptp.sub @t152 @t216)) % 1.12/1.30 (define @t218 () (_ @t93 tptp.id @t217 tptp.id)) % 1.12/1.30 (define @t219 () (_ @t93 tptp.id @t2 tptp.id)) % 1.12/1.30 (define @t220 () (not @t219)) % 1.12/1.30 (define @t221 () (or @t220 @t218)) % 1.12/1.30 (define @t222 () (forall @t62 @t221)) % 1.12/1.30 (define @t223 () (not @t222)) % 1.12/1.30 (define @t224 () (_ @t93 tptp.id @t158 tptp.id)) % 1.12/1.30 (define @t225 () (_ @t78 tptp.id @t5)) % 1.12/1.30 (define @t226 () (_ @t93 tptp.id @t225 tptp.id)) % 1.12/1.30 (define @t227 () (_ @t93 tptp.id @t5 tptp.id)) % 1.12/1.30 (define @t228 () (not @t227)) % 1.12/1.30 (define @t229 () (or @t228 @t226)) % 1.12/1.30 (define @t230 () (forall @t14 @t229)) % 1.12/1.30 (define @t231 () (not @t230)) % 1.12/1.30 (define @t232 () (or @t167 @t231 @t224)) % 1.12/1.30 (define @t233 () (forall @t90 @t232)) % 1.12/1.30 (define @t234 () (not @t233)) % 1.12/1.30 (define @t235 () (or @t234 @t223 @t215)) % 1.12/1.30 (define @t236 () (forall @t169 @t235)) % 1.12/1.30 (define @t237 () (_ @t93 tptp.id @t172 tptp.id)) % 1.12/1.30 (define @t238 () (tptp.sub @t171 @t216)) % 1.12/1.30 (define @t239 () (_ @t93 tptp.id @t238 tptp.id)) % 1.12/1.30 (define @t240 () (or @t220 @t239)) % 1.12/1.30 (define @t241 () (forall @t62 @t240)) % 1.12/1.30 (define @t242 () (not @t241)) % 1.12/1.30 (define @t243 () (or @t234 @t242 @t237)) % 1.12/1.30 (define @t244 () (forall @t174 @t243)) % 1.12/1.30 (define @t245 () (=> @t244 @t236)) % 1.12/1.30 (define @t246 () (= tptp.id @t32)) % 1.12/1.30 (define @t247 () (=> @t246 @t245)) % 1.12/1.30 (define @t248 () (tptp.sub @t5 tptp.id)) % 1.12/1.30 (define @t249 () (= @t5 @t248)) % 1.12/1.30 (define @t250 () (forall @t14 @t249)) % 1.12/1.30 (define @t251 () (or @t223 @t215)) % 1.12/1.30 (define @t252 () (or @t234 @t251)) % 1.12/1.30 (define @t253 () (forall @t169 @t252)) % 1.12/1.30 (define @t254 () (@list @t152)) % 1.12/1.30 (define @t255 () (forall @t254 @t252)) % 1.12/1.30 (define @t256 () (forall @t254 @t251)) % 1.12/1.30 (define @t257 () (@list @t5)) % 1.12/1.30 (define @t258 () (or @t234 @t256)) % 1.12/1.30 (define @t259 () (tptp.lam @t5)) % 1.12/1.30 (define @t260 () (_ @t93 tptp.id @t259 tptp.id)) % 1.12/1.30 (define @t261 () (tptp.sub @t5 @t216)) % 1.12/1.30 (define @t262 () (_ @t93 tptp.id @t261 tptp.id)) % 1.12/1.30 (define @t263 () (forall @t62 (or @t220 @t262))) % 1.12/1.30 (define @t264 () (not @t263)) % 1.12/1.30 (define @t265 () (forall @t14 (or @t264 @t260))) % 1.12/1.30 (define @t266 () (or @t264 @t127)) % 1.12/1.30 (define @t267 () (not @t106)) % 1.12/1.30 (define @t268 () (or @t267 @t120)) % 1.12/1.30 (define @t269 () (_ (_ @t97 @t147) tptp.id)) % 1.12/1.30 (define @t270 () (or @t167 @t231 @t269)) % 1.12/1.30 (define @t271 () (=> @t230 @t269)) % 1.12/1.30 (define @t272 () (lambda @t14 (_ @t137 @t5))) % 1.12/1.30 (define @t273 () (_ @t83 tptp.sh)) % 1.12/1.30 (define @t274 () (lambda @t90 @t147)) % 1.12/1.30 (define @t275 () (_ @t148 tptp.id)) % 1.12/1.30 (define @t276 () (not @t98)) % 1.12/1.30 (define @t277 () (or @t276 @t109)) % 1.12/1.30 (define @t278 () (=> @t110 (_ (_ @t97 (_ @t275 @t83)) tptp.id))) % 1.12/1.30 (define @t279 () (=> @t89 @t278)) % 1.12/1.30 (define @t280 () (forall @t90 @t279)) % 1.12/1.30 (define @t281 () (=> @t280 @t129)) % 1.12/1.30 (define @t282 () (forall @t95 @t281)) % 1.12/1.30 (define @t283 () (or @t242 @t237)) % 1.12/1.30 (define @t284 () (or @t234 @t283)) % 1.12/1.30 (define @t285 () (forall @t174 @t284)) % 1.12/1.30 (define @t286 () (@list @t171)) % 1.12/1.30 (define @t287 () (forall @t286 @t284)) % 1.12/1.30 (define @t288 () (forall @t286 @t283)) % 1.12/1.30 (define @t289 () (or @t234 @t288)) % 1.12/1.30 (define @t290 () (tptp.sub @t5 @t151)) % 1.12/1.30 (define @t291 () (tptp.lam @t290)) % 1.12/1.30 (define @t292 () (_ @t93 tptp.id @t291 tptp.id)) % 1.12/1.30 (define @t293 () (forall @t14 (or @t264 @t292))) % 1.12/1.30 (define @t294 () (or @t264 @t119)) % 1.12/1.30 (define @t295 () (=> @t280 @t123)) % 1.12/1.30 (define @t296 () (forall @t95 @t295)) % 1.12/1.30 (define @t297 () (= @t5 @t13)) % 1.12/1.30 (define @t298 () (@quantifiers_skolemize @t170 1)) % 1.12/1.30 (define @t299 () (@quantifiers_skolemize @t170 0)) % 1.12/1.30 (define @t300 () (_ @t299 @t151 (tptp.lam @t298) @t151)) % 1.12/1.30 (define @t301 () (tptp.sub @t298 @t154)) % 1.12/1.30 (define @t302 () (_ @t299 @t151 @t301 @t151)) % 1.12/1.30 (define @t303 () (_ @t299 @t151 @t2 @t151)) % 1.12/1.30 (define @t304 () (forall @t62 (or (not @t303) @t302))) % 1.12/1.30 (define @t305 () (not @t304)) % 1.12/1.30 (define @t306 () (_ @t299 @t151 @t158 @t151)) % 1.12/1.30 (define @t307 () (_ @t299 @t151 @t159 @t151)) % 1.12/1.30 (define @t308 () (_ @t299 @t151 @t5 @t151)) % 1.12/1.30 (define @t309 () (forall @t90 (or @t167 (not (forall @t14 (or (not @t308) @t307))) @t306))) % 1.12/1.30 (define @t310 () (not @t309)) % 1.12/1.30 (define @t311 () (or @t310 @t305 @t300)) % 1.12/1.30 (define @t312 () (@list true)) % 1.12/1.30 (define @t313 () (@list @t311)) % 1.12/1.30 (define @t314 () (tptp.lam (tptp.sub @t298 @t151))) % 1.12/1.30 (define @t315 () (_ @t299 @t151 @t314 @t151)) % 1.12/1.30 (define @t316 () (or @t310 @t305 @t315)) % 1.12/1.30 (define @t317 () (not @t316)) % 1.12/1.30 (define @t318 () (@var "BOUND_VARIABLE_12595" tptp.subst)) % 1.12/1.30 (define @t319 () (@var "BOUND_VARIABLE_12596" tptp.term)) % 1.12/1.30 (define @t320 () (lambda (@list @t318 @t319 (@var "BOUND_VARIABLE_12597" tptp.subst)) (_ @t299 @t318 @t319 @t318))) % 1.12/1.30 (define @t321 () (_ @t320 @t151 @t314 @t151)) % 1.12/1.30 (define @t322 () (_ @t320 @t151 @t301 @t151)) % 1.12/1.30 (define @t323 () (_ @t320 @t151 @t2 @t151)) % 1.12/1.30 (define @t324 () (not @t323)) % 1.12/1.30 (define @t325 () (or @t324 @t322)) % 1.12/1.30 (define @t326 () (forall @t62 @t325)) % 1.12/1.30 (define @t327 () (not @t326)) % 1.12/1.30 (define @t328 () (_ @t320 @t151 @t158 @t151)) % 1.12/1.30 (define @t329 () (_ @t320 @t151 @t159 @t151)) % 1.12/1.30 (define @t330 () (_ @t320 @t151 @t5 @t151)) % 1.12/1.30 (define @t331 () (not @t330)) % 1.12/1.30 (define @t332 () (or @t331 @t329)) % 1.12/1.30 (define @t333 () (forall @t14 @t332)) % 1.12/1.30 (define @t334 () (not @t333)) % 1.12/1.30 (define @t335 () (or @t167 @t334 @t328)) % 1.12/1.30 (define @t336 () (forall @t90 @t335)) % 1.12/1.30 (define @t337 () (not @t336)) % 1.12/1.30 (define @t338 () (or @t337 @t327 @t321)) % 1.12/1.30 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 1.12/1.30 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 1.12/1.30 (assume @p3 @t16) % 1.12/1.30 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t19) @t1) (_ tptp.lam (_ @t6 (_ @t18 (_ @t17 tptp.sh)))))))) % 1.12/1.30 (assume @p5 (= tptp.axclos @t23)) % 1.12/1.30 (assume @p6 (= tptp.axidl @t25)) % 1.12/1.30 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t26 @t10) @t1)))) % 1.12/1.30 (assume @p8 (= tptp.axassoc @t28)) % 1.12/1.30 (assume @p9 (= tptp.axmap (forall @t22 (= (_ (_ tptp.comp @t10) @t20) @t30)))) % 1.12/1.30 (assume @p10 (= tptp.axidr @t31)) % 1.12/1.30 (assume @p11 @t33) % 1.12/1.30 (assume @p12 (= tptp.axscons (forall @t24 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t26 @t1)) @t1)))) % 1.12/1.30 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 1.12/1.30 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t35 (_ tptp.var @t34))))) % 1.12/1.30 (assume @p15 (= tptp.ulamvarind (forall @t39 (=> (_ @t36 tptp.one) (=> (forall @t14 (=> @t35 (=> @t37 (_ @t36 @t34)))) @t38))))) % 1.12/1.30 (assume @p16 (= tptp.apinj1 (forall @t45 (=> @t44 @t40)))) % 1.12/1.30 (assume @p17 (= tptp.apinj2 (forall @t45 (=> @t44 @t46)))) % 1.12/1.30 (assume @p18 (= tptp.laminj (forall @t47 (=> (= @t19 (_ tptp.lam @t2)) @t40)))) % 1.12/1.30 (assume @p19 (= tptp.shinj (forall @t47 (=> (= @t34 (_ @t3 tptp.sh)) @t40)))) % 1.12/1.30 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t43) (not (= @t19 (_ @t42 @t43)))))) % 1.12/1.30 (assume @p21 (= tptp.apnotvar (forall @t47 (not (_ tptp.var @t9))))) % 1.12/1.30 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t19))))) % 1.12/1.30 (assume @p23 (= tptp.induction (forall @t39 (=> @t38 (=> @t51 (=> (forall @t14 (=> @t37 @t49)) @t48)))))) % 1.12/1.30 (assume @p24 (= tptp.pushprop_lem0 (forall @t55 (exists @t54 @t53)))) % 1.12/1.30 (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))))))))))))))))))))))))) % 1.12/1.30 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 1.12/1.30 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t36 @t57 @t5 @t1 @t2) (=> @t37 (_ @t57 (_ @t6 (_ @t56 @t1))))))) % 1.12/1.30 (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))))))))))))))))))))))))) % 1.12/1.30 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 1.12/1.30 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t58 (=> @t37 (=> @t53 (_ @t52 tptp.one)))))) % 1.12/1.30 (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))))))))))))))))))))))))) % 1.12/1.30 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 1.12/1.30 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t58 (=> @t53 (=> @t63 (forall @t60 (=> (_ tptp.var @t43) (=> (_ @t52 @t43) (_ @t52 (_ @t59 tptp.sh)))))))))) % 1.12/1.30 (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))))))))))))))))))))))))) % 1.12/1.30 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 1.12/1.30 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t58 (=> @t53 (=> (forall @t62 (=> @t61 @t66)) @t65))))) % 1.12/1.30 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 1.12/1.30 (assume @p38 (= tptp.pushprop (forall @t55 (=> @t63 (=> @t37 @t65))))) % 1.12/1.30 (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))))))))))))))))))))))))) % 1.12/1.30 (assume @p40 (= tptp.pushprop_lthm_orig @t67)) % 1.12/1.30 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t67))) % 1.12/1.30 (assume @p42 (= tptp.induction2lem (forall @t39 (=> @t51 (=> @t70 (forall @t12 (=> @t63 (_ @t36 @t7)))))))) % 1.12/1.30 (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 @t71)))))))))))))))))))))))) % 1.12/1.30 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t71)))))))))) % 1.12/1.30 (assume @p45 (= tptp.induction2 (forall @t39 (=> @t38 (=> @t51 (=> @t70 @t48)))))) % 1.12/1.30 (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 @t72)))))))))))))))))))))))))) % 1.12/1.30 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t72))) % 1.12/1.30 (assume @p48 (= tptp.substmonoid (and @t28 @t25 @t31))) % 1.12/1.30 (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)))))))))))))))))))))))))))) % 1.12/1.30 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 1.12/1.30 (assume @p51 (= tptp.termmset (and @t23 @t15))) % 1.12/1.30 (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))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 1.12/1.30 (assume @p54 (= tptp.hoasapinj1 (forall @t45 (=> @t75 @t40)))) % 1.12/1.30 (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)))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 1.12/1.30 (assume @p57 (= tptp.hoasapinj2 (forall @t45 (=> @t75 @t46)))) % 1.12/1.30 (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))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 1.12/1.30 (assume @p60 (= tptp.hoaslaminj (forall @t90 (=> @t89 (forall (@list @t76) (=> (forall @t85 (= (_ (_ tptp.sub @t77) @t20) (_ (_ @t76 @t21) @t29))) (=> (= @t84 (_ @t82 (lambda @t81 @t77))) (forall @t81 (= @t80 @t77))))))))) % 1.12/1.30 (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)))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 1.12/1.30 (assume @p63 (= tptp.hoaslamnotap (forall @t90 (=> @t89 (forall @t47 (not (= (_ @t82 (lambda (@list @t1 @t43) (_ @t79 @t43))) @t91))))))) % 1.12/1.30 (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))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 1.12/1.30 (assume @p66 (= tptp.hoaslamnotvar (forall @t90 (=> @t89 (not (_ (_ @t92 @t84) tptp.id)))))) % 1.12/1.30 (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)))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 1.12/1.30 (assume @p69 (= tptp.hoasapnotvar (forall @t47 (not (_ (_ @t92 @t91) tptp.id))))) % 1.12/1.30 (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))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 1.12/1.30 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t95 (exists @t54 @t94)))) % 1.12/1.30 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 1.12/1.30 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t105 (=> @t104 (=> @t103 (=> @t99 (=> @t94 (forall @t14 (=> @t35 @t96))))))))) % 1.12/1.30 (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)))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t105 (=> @t104 (=> @t103 (=> @t107 (=> @t94 (forall @t47 (=> @t96 (=> @t66 (_ @t52 @t9))))))))))) % 1.12/1.30 (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)))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t62 (exists @t90 (forall @t12 (= @t80 @t64)))))) % 1.12/1.30 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 1.12/1.30 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t105 (=> @t104 (=> @t103 @t114))))) % 1.12/1.30 (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)))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 1.12/1.30 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t105 @t114))) % 1.12/1.30 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 1.12/1.30 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t95 (=> @t104 (=> @t103 (=> @t99 (forall @t14 (=> @t35 @t98)))))))) % 1.12/1.30 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t115)) % 1.12/1.30 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t115)) % 1.12/1.30 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t95 (=> @t104 (=> @t103 (=> @t107 (forall @t47 (=> @t98 (=> @t106 (_ (_ @t97 @t9) tptp.id)))))))))) % 1.12/1.30 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t116)) % 1.12/1.30 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t116)) % 1.12/1.30 (assume @p91 @t126) % 1.12/1.30 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 1.12/1.30 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t95 (=> (forall @t90 (=> (exists @t60 (forall @t85 (and (= @t87 (_ (_ tptp.sub (_ @t59 @t10)) @t20)) (= (_ @t59 @t30) @t86)))) @t111)) @t123)))) % 1.12/1.30 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t95 (=> @t104 (=> @t103 @t130))))) % 1.12/1.30 (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)))))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 1.12/1.30 (assume @p97 @t132) % 1.12/1.30 (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)))))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p99 @t136) % 1.12/1.30 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t62 (exists @t90 (= (_ @t3 @t32) @t138))))) % 1.12/1.30 (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)))))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 1.12/1.30 (assume @p103 (= tptp.hoasinduction (forall @t95 (=> @t104 (=> @t103 (=> @t99 @t139)))))) % 1.12/1.30 (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 @t140)))))))))))))))))))))))))))))))))))) % 1.12/1.30 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t140))) % 1.12/1.30 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 1.12/1.30 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t95 @t139))) % 1.12/1.30 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 1.12/1.30 (assume @p109 @t141) % 1.12/1.30 (assume @p110 true) % 1.12/1.30 (step @p111 (= tptp.pushprop_p_and_p_prime @t145) :rule refl :args (@t145)) % 1.12/1.30 (step @p112 (= tptp.hoasap @t146) :rule refl :args (@t146)) % 1.12/1.30 (step @p113 (= tptp.hoaslam @t148) :rule refl :args (@t148)) % 1.12/1.30 (step @p114 (= tptp.hoasvar @t149) :rule refl :args (@t149)) % 1.12/1.30 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t150) :rule refl :args (@t150)) % 1.12/1.30 (step @p116 :rule bool-impl-true2 :args ((=> @t175 @t170))) % 1.12/1.30 (step @p117 :rule refl :args (@t151)) % 1.12/1.30 (step @p118 :rule refl :args (@t32)) % 1.12/1.30 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t32 @t151))) % 1.12/1.30 (step @p120 :rule symm :premises (@p119)) % 1.12/1.30 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 1.12/1.30 (step @p122 :rule refl :args (@t153)) % 1.12/1.30 (step @p123 :rule cong :premises (@p121 @p122 @p121) :args (@t176)) % 1.12/1.30 (step @p124 :rule refl :args (@t156)) % 1.12/1.30 (step @p125 :rule refl :args (@t168)) % 1.12/1.30 (step @p126 :rule nary_cong :premises (@p125 @p124 @p123) :args (@t177)) % 1.12/1.30 (step @p127 :rule cong :premises (@p126) :args ((forall @t169 @t177))) % 1.12/1.30 (step @p128 :rule refl :args (@t176)) % 1.12/1.30 (step @p129 :rule refl :args (@t2)) % 1.12/1.30 (step @p130 :rule cong :premises (@p129 @p121) :args (@t178)) % 1.12/1.30 (step @p131 :rule refl :args (@t152)) % 1.12/1.30 (step @p132 :rule cong :premises (@p131 @p130) :args (@t179)) % 1.12/1.30 (step @p133 :rule cong :premises (@p121 @p132 @p121) :args (@t180)) % 1.12/1.30 (step @p134 :rule cong :premises (@p121 @p129 @p121) :args (@t181)) % 1.12/1.30 (step @p135 :rule cong :premises (@p134) :args (@t182)) % 1.12/1.30 (step @p136 :rule nary_cong :premises (@p135 @p133) :args (@t183)) % 1.12/1.30 (step @p137 :rule cong :premises (@p136) :args (@t184)) % 1.12/1.30 (step @p138 :rule cong :premises (@p137) :args (@t185)) % 1.12/1.30 (step @p139 :rule refl :args (@t158)) % 1.12/1.30 (step @p140 :rule cong :premises (@p121 @p139 @p121) :args (@t186)) % 1.12/1.30 (step @p141 :rule refl :args (@t160)) % 1.12/1.30 (step @p142 :rule refl :args (@t167)) % 1.12/1.30 (step @p143 :rule nary_cong :premises (@p142 @p141 @p140) :args (@t187)) % 1.12/1.30 (step @p144 :rule cong :premises (@p143) :args ((forall @t90 @t187))) % 1.12/1.30 (step @p145 :rule refl :args (@t186)) % 1.12/1.30 (step @p146 :rule refl :args (@t5)) % 1.12/1.30 (step @p147 :rule cong :premises (@p121 @p146) :args (@t188)) % 1.12/1.30 (step @p148 :rule cong :premises (@p121 @p147 @p121) :args (@t189)) % 1.12/1.30 (step @p149 :rule cong :premises (@p121 @p146 @p121) :args (@t190)) % 1.12/1.30 (step @p150 :rule cong :premises (@p149) :args (@t191)) % 1.12/1.30 (step @p151 :rule nary_cong :premises (@p150 @p148) :args (@t192)) % 1.12/1.30 (step @p152 :rule cong :premises (@p151) :args (@t193)) % 1.12/1.30 (step @p153 :rule cong :premises (@p152) :args (@t194)) % 1.12/1.30 (step @p154 :rule refl :args (@t167)) % 1.12/1.30 (step @p155 :rule nary_cong :premises (@p154 @p153 @p145) :args (@t195)) % 1.12/1.30 (step @p156 :rule cong :premises (@p155) :args (@t196)) % 1.12/1.30 (step @p157 :rule trans :premises (@p156 @p144)) % 1.12/1.30 (step @p158 :rule cong :premises (@p157) :args (@t197)) % 1.12/1.30 (step @p159 :rule nary_cong :premises (@p158 @p138 @p128) :args (@t198)) % 1.12/1.30 (step @p160 :rule cong :premises (@p159) :args (@t199)) % 1.12/1.30 (step @p161 :rule trans :premises (@p160 @p127)) % 1.12/1.30 (step @p162 :rule refl :args (@t172)) % 1.12/1.30 (step @p163 :rule cong :premises (@p121 @p162 @p121) :args (@t200)) % 1.12/1.30 (step @p164 :rule refl :args (@t173)) % 1.12/1.30 (step @p165 :rule nary_cong :premises (@p125 @p164 @p163) :args (@t201)) % 1.12/1.30 (step @p166 :rule cong :premises (@p165) :args ((forall @t174 @t201))) % 1.12/1.30 (step @p167 :rule refl :args (@t200)) % 1.12/1.30 (step @p168 :rule refl :args (@t171)) % 1.12/1.30 (step @p169 :rule cong :premises (@p168 @p130) :args (@t202)) % 1.12/1.30 (step @p170 :rule cong :premises (@p121 @p169 @p121) :args (@t203)) % 1.12/1.30 (step @p171 :rule nary_cong :premises (@p135 @p170) :args (@t204)) % 1.12/1.30 (step @p172 :rule cong :premises (@p171) :args (@t205)) % 1.12/1.30 (step @p173 :rule cong :premises (@p172) :args (@t206)) % 1.12/1.30 (step @p174 :rule nary_cong :premises (@p158 @p173 @p167) :args (@t207)) % 1.12/1.30 (step @p175 :rule cong :premises (@p174) :args (@t208)) % 1.12/1.30 (step @p176 :rule trans :premises (@p175 @p166)) % 1.12/1.30 (step @p177 :rule cong :premises (@p176 @p161) :args (@t209)) % 1.12/1.30 (step @p178 :rule eq-refl :args (@t32)) % 1.12/1.30 (step @p179 :rule cong :premises (@p178 @p177) :args (@t210)) % 1.12/1.30 (step @p180 :rule trans :premises (@p179 @p116)) % 1.12/1.30 (step @p181 :rule cong :premises (@p146 @p121) :args (@t211)) % 1.12/1.30 (step @p182 :rule cong :premises (@p146 @p181) :args (@t212)) % 1.12/1.30 (step @p183 :rule cong :premises (@p182) :args (@t213)) % 1.12/1.30 (step @p184 :rule cong :premises (@p183 @p180) :args (@t214)) % 1.12/1.30 (step @p185 :rule cong :premises (@p184) :args ((not @t214))) % 1.12/1.30 (step @p186 :rule eq-symm :args (@t32 tptp.id)) % 1.12/1.30 (step @p187 :rule refl :args (tptp.axvarshift)) % 1.12/1.30 (step @p188 :rule cong :premises (@p187 @p186) :args (@t33)) % 1.12/1.30 (step @p189 :rule eq_resolve :premises (@p11 @p188)) % 1.12/1.30 (step @p190 :rule equiv_elim2 :premises (@p99)) % 1.12/1.30 (step @p191 :rule resolution :premises (@p190 @p109) :args (true tptp.hoasinduction_lem3a_lthm)) % 1.12/1.30 (step @p192 :rule not_implies_elim2 :premises (@p191)) % 1.12/1.30 (step @p193 :rule not_implies_elim1 :premises (@p192)) % 1.12/1.30 (step @p194 :rule eq_resolve :premises (@p193 @p189)) % 1.12/1.30 (step @p195 :rule refl :args (@t153)) % 1.12/1.30 (step @p196 :rule cong :premises (@p194 @p195 @p194) :args (@t215)) % 1.12/1.30 (step @p197 :rule refl :args (@t2)) % 1.12/1.30 (step @p198 :rule cong :premises (@p197 @p194) :args (@t216)) % 1.12/1.30 (step @p199 :rule refl :args (@t152)) % 1.12/1.30 (step @p200 :rule cong :premises (@p199 @p198) :args (@t217)) % 1.12/1.30 (step @p201 :rule cong :premises (@p194 @p200 @p194) :args (@t218)) % 1.12/1.30 (step @p202 :rule cong :premises (@p194 @p197 @p194) :args (@t219)) % 1.12/1.30 (step @p203 :rule cong :premises (@p202) :args (@t220)) % 1.12/1.30 (step @p204 :rule nary_cong :premises (@p203 @p201) :args (@t221)) % 1.12/1.30 (step @p205 :rule cong :premises (@p204) :args (@t222)) % 1.12/1.30 (step @p206 :rule cong :premises (@p205) :args (@t223)) % 1.12/1.30 (step @p207 :rule refl :args (@t158)) % 1.12/1.30 (step @p208 :rule cong :premises (@p194 @p207 @p194) :args (@t224)) % 1.12/1.30 (step @p209 :rule refl :args (@t5)) % 1.12/1.30 (step @p210 :rule cong :premises (@p194 @p209) :args (@t225)) % 1.12/1.30 (step @p211 :rule cong :premises (@p194 @p210 @p194) :args (@t226)) % 1.12/1.30 (step @p212 :rule cong :premises (@p194 @p209 @p194) :args (@t227)) % 1.12/1.30 (step @p213 :rule cong :premises (@p212) :args (@t228)) % 1.12/1.30 (step @p214 :rule nary_cong :premises (@p213 @p211) :args (@t229)) % 1.12/1.30 (step @p215 :rule cong :premises (@p214) :args (@t230)) % 1.12/1.30 (step @p216 :rule cong :premises (@p215) :args (@t231)) % 1.12/1.30 (step @p217 :rule nary_cong :premises (@p154 @p216 @p208) :args (@t232)) % 1.12/1.30 (step @p218 :rule cong :premises (@p217) :args (@t233)) % 1.12/1.30 (step @p219 :rule cong :premises (@p218) :args (@t234)) % 1.12/1.30 (step @p220 :rule nary_cong :premises (@p219 @p206 @p196) :args (@t235)) % 1.12/1.30 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(step @p464 :rule ho_cong :premises (@p463 @p362)) % 1.12/1.30 (step @p465 :rule refl :args (@t110)) % 1.12/1.30 (step @p466 :rule cong :premises (@p465 @p464) :args (@t111)) % 1.12/1.30 (step @p467 :rule refl :args (@t89)) % 1.12/1.30 (step @p468 :rule cong :premises (@p467 @p466) :args (@t112)) % 1.12/1.30 (step @p469 :rule cong :premises (@p468) :args (@t113)) % 1.12/1.30 (step @p470 :rule cong :premises (@p469 @p460) :args (@t130)) % 1.12/1.30 (step @p471 :rule cong :premises (@p470) :args (@t131)) % 1.12/1.30 (step @p472 :rule cong :premises (@p458 @p471) :args (@t132)) % 1.12/1.30 (step @p473 :rule trans :premises (@p472 @p459)) % 1.12/1.30 (step @p474 :rule eq_resolve :premises (@p97 @p473)) % 1.12/1.30 (step @p475 :rule aci_norm :args ((= @t284 @t243))) % 1.12/1.30 (step @p476 :rule cong :premises (@p475) :args (@t285)) % 1.12/1.30 (step @p477 :rule quant-merge-prenex :args ((= (forall @t95 @t287) @t285))) % 1.12/1.30 (step @p478 :rule alpha_equiv :args (@t288 (@list @t171) @t257)) % 1.12/1.30 (step @p479 :rule nary_cong :premises (@p244 @p478) :args (@t289)) % 1.12/1.30 (step @p480 :rule quant-miniscope-or :args ((= @t287 @t289))) % 1.12/1.30 (step @p481 :rule trans :premises (@p480 @p479)) % 1.12/1.30 (step @p482 :rule symm :premises (@p481)) % 1.12/1.30 (step @p483 :rule cong :premises (@p482) :args ((forall @t95 (or @t234 @t293)))) % 1.12/1.30 (step @p484 :rule trans :premises (@p483 @p477)) % 1.12/1.30 (step @p485 :rule trans :premises (@p484 @p476)) % 1.12/1.30 (step @p486 :rule bool-impl-elim :args (@t233 @t293)) % 1.12/1.30 (step @p487 :rule cong :premises (@p486) :args ((forall @t95 (=> @t233 @t293)))) % 1.12/1.30 (step @p488 :rule trans :premises (@p487 @p485)) % 1.12/1.30 (step @p489 :rule refl :args ((_ @t93 tptp.id @t118 tptp.id))) % 1.12/1.30 (step @p490 :rule refl :args ((tptp.lam @t117))) % 1.12/1.30 (step @p491 :rule refl :args (@t211)) % 1.12/1.30 (step @p492 :rule cong :premises (@p146 @p117) :args (@t290)) % 1.12/1.30 (step @p493 :rule trans :premises (@p492 @p491)) % 1.12/1.30 (step @p494 :rule cong :premises (@p493) :args (@t291)) % 1.12/1.30 (step @p495 :rule trans :premises (@p494 @p490)) % 1.12/1.30 (step @p496 :rule cong :premises (@p256 @p495 @p256) :args (@t292)) % 1.12/1.30 (step @p497 :rule trans :premises (@p496 @p489)) % 1.12/1.30 (step @p498 :rule ho_cong :premises (@p260 @p495)) % 1.12/1.30 (step @p499 :rule ho_cong :premises (@p498 @p256)) % 1.12/1.30 (step @p500 :rule cong :premises (@p499 @p497) :args ((= (_ (_ @t97 @t291) tptp.id) @t292))) % 1.12/1.30 (step @p501 :rule symm :premises (@p500)) % 1.12/1.30 (step @p502 :rule refl :args (@t119)) % 1.12/1.30 (step @p503 :rule eq_resolve :premises (@p502 @p501)) % 1.12/1.30 (step @p504 :rule ho_cong :premises (@p336 @p493)) % 1.12/1.30 (step @p505 :rule cong :premises (@p504 @p495) :args ((= (_ tptp.lam @t290) @t291))) % 1.12/1.30 (step @p506 :rule symm :premises (@p505)) % 1.12/1.30 (step @p507 :rule refl :args (@t118)) % 1.12/1.30 (step @p508 :rule eq_resolve :premises (@p507 @p506)) % 1.12/1.30 (step @p509 :rule ho_cong :premises (@p294 @p117)) % 1.12/1.30 (step @p510 :rule cong :premises (@p509 @p493) :args ((= (_ @t6 @t151) @t290))) % 1.12/1.30 (step @p511 :rule symm :premises (@p510)) % 1.12/1.30 (step @p512 :rule refl :args (@t117)) % 1.12/1.30 (step @p513 :rule eq_resolve :premises (@p512 @p511)) % 1.12/1.30 (step @p514 :rule ho_cong :premises (@p294 @p121)) % 1.12/1.30 (step @p515 :rule trans :premises (@p514 @p513)) % 1.12/1.30 (step @p516 :rule ho_cong :premises (@p336 @p515)) % 1.12/1.30 (step @p517 :rule trans :premises (@p516 @p508)) % 1.12/1.30 (step @p518 :rule ho_cong :premises (@p260 @p517)) % 1.12/1.30 (step @p519 :rule ho_cong :premises (@p518 @p256)) % 1.12/1.30 (step @p520 :rule trans :premises (@p519 @p503)) % 1.12/1.30 (step @p521 :rule nary_cong :premises (@p274 @p520) :args (@t294)) % 1.12/1.30 (step @p522 :rule cong :premises (@p521) :args ((forall @t14 @t294))) % 1.12/1.30 (step @p523 :rule bool-impl-elim :args (@t263 @t119)) % 1.12/1.30 (step @p524 :rule cong :premises (@p523) :args ((forall @t14 (=> @t263 @t119)))) % 1.12/1.30 (step @p525 :rule trans :premises (@p524 @p522)) % 1.12/1.30 (step @p526 :rule refl :args (@t119)) % 1.12/1.30 (step @p527 :rule cong :premises (@p319 @p526) :args (@t122)) % 1.12/1.30 (step @p528 :rule cong :premises (@p527) :args (@t123)) % 1.12/1.30 (step @p529 :rule trans :premises (@p528 @p525)) % 1.12/1.30 (step @p530 :rule cong :premises (@p454 @p529) :args (@t295)) % 1.12/1.30 (step @p531 :rule cong :premises (@p530) :args (@t296)) % 1.12/1.30 (step @p532 :rule trans :premises (@p531 @p488)) % 1.12/1.30 (step @p533 :rule refl :args (tptp.hoasinduction_lem3aa)) % 1.12/1.30 (step @p534 :rule cong :premises (@p533 @p532) :args ((= tptp.hoasinduction_lem3aa @t296))) % 1.12/1.30 (step @p535 :rule refl :args (@t123)) % 1.12/1.30 (step @p536 :rule cong :premises (@p469 @p535) :args (@t124)) % 1.12/1.30 (step @p537 :rule cong :premises (@p536) :args (@t125)) % 1.12/1.30 (step @p538 :rule cong :premises (@p533 @p537) :args (@t126)) % 1.12/1.30 (step @p539 :rule trans :premises (@p538 @p534)) % 1.12/1.30 (step @p540 :rule eq_resolve :premises (@p91 @p539)) % 1.12/1.30 (step @p541 :rule cong :premises (@p540 @p474) :args (@t133)) % 1.12/1.30 (step @p542 :rule cong :premises (@p189 @p541) :args (@t134)) % 1.12/1.30 (step @p543 :rule refl :args (@t248)) % 1.12/1.30 (step @p544 :rule refl :args (@t13)) % 1.12/1.30 (step @p545 :rule cong :premises (@p544 @p543) :args ((= @t13 @t248))) % 1.12/1.30 (step @p546 :rule symm :premises (@p545)) % 1.12/1.30 (step @p547 :rule eq_resolve :premises (@p544 @p546)) % 1.12/1.30 (step @p548 :rule cong :premises (@p146 @p547) :args (@t297)) % 1.12/1.30 (step @p549 :rule cong :premises (@p548) :args ((forall @t14 @t297))) % 1.12/1.30 (step @p550 :rule eq-symm :args (@t13 @t5)) % 1.12/1.30 (step @p551 :rule cong :premises (@p550) :args (@t15)) % 1.12/1.30 (step @p552 :rule trans :premises (@p551 @p549)) % 1.12/1.30 (step @p553 :rule refl :args (tptp.axvarid)) % 1.12/1.30 (step @p554 :rule cong :premises (@p553 @p552) :args (@t16)) % 1.12/1.30 (step @p555 :rule eq_resolve :premises (@p3 @p554)) % 1.12/1.30 (step @p556 :rule cong :premises (@p555 @p542) :args (@t135)) % 1.12/1.30 (step @p557 :rule refl :args (tptp.hoasinduction_lem3a_lthm)) % 1.12/1.30 (step @p558 :rule cong :premises (@p557 @p556) :args (@t136)) % 1.12/1.30 (step @p559 :rule eq_resolve :premises (@p99 @p558)) % 1.12/1.30 (step @p560 :rule trans :premises (@p559 @p239)) % 1.12/1.30 (step @p561 :rule cong :premises (@p560) :args (@t141)) % 1.12/1.30 (step @p562 :rule trans :premises (@p561 @p185)) % 1.12/1.30 (step @p563 :rule eq_resolve :premises (@p109 @p562)) % 1.12/1.30 (step @p564 :rule not_implies_elim2 :premises (@p563)) % 1.12/1.30 (step @p565 :rule not_implies_elim1 :premises (@p564)) % 1.12/1.30 (step @p566 :rule not_implies_elim2 :premises (@p564)) % 1.12/1.30 (step @p567 :rule skolemize :premises (@p566)) % 1.12/1.30 (step @p568 :rule cnf_or_neg :args (@t311 2)) % 1.12/1.30 (step @p569 :rule chain_m_resolution :premises (@p568 @p567) :args ((not @t300) @t312 @t313)) % 1.12/1.30 (step @p570 :rule false_intro :premises (@p569)) % 1.12/1.30 (step @p571 :rule refl :args (@t151)) % 1.12/1.30 (step @p572 :rule not_implies_elim1 :premises (@p563)) % 1.12/1.30 (step @p573 :rule instantiate :premises (@p572) :args ((@list @t298))) % 1.12/1.30 (step @p574 :rule symm :premises (@p573)) % 1.12/1.30 (step @p575 :rule cong :premises (@p574) :args (@t314)) % 1.12/1.30 (step @p576 :rule cong :premises (@p571 @p575 @p571) :args (@t315)) % 1.12/1.30 (step @p577 :rule trans :premises (@p576 @p570)) % 1.12/1.30 (step @p578 :rule false_elim :premises (@p577)) % 1.12/1.30 (step @p579 :rule bool-double-not-elim :args (@t304)) % 1.12/1.30 (step @p580 :rule refl :args (@t311)) % 1.12/1.30 (step @p581 :rule nary_cong :premises (@p580 @p579) :args ((or @t311 (not @t305)))) % 1.12/1.30 (step @p582 :rule cnf_or_neg :args (@t311 1)) % 1.12/1.30 (step @p583 :rule eq_resolve :premises (@p582 @p581)) % 1.12/1.30 (step @p584 :rule reordering :premises (@p583) :args ((or @t304 @t311))) % 1.12/1.30 (step @p585 :rule chain_m_resolution :premises (@p584 @p567) :args (@t304 @t312 @t313)) % 1.12/1.30 (step @p586 :rule bool-double-not-elim :args (@t309)) % 1.12/1.30 (step @p587 :rule nary_cong :premises (@p580 @p586) :args ((or @t311 (not @t310)))) % 1.12/1.30 (step @p588 :rule cnf_or_neg :args (@t311 0)) % 1.12/1.30 (step @p589 :rule eq_resolve :premises (@p588 @p587)) % 1.12/1.30 (step @p590 :rule reordering :premises (@p589) :args ((or @t309 @t311))) % 1.12/1.30 (step @p591 :rule chain_m_resolution :premises (@p590 @p567) :args (@t309 @t312 @t313)) % 1.12/1.30 (step @p592 :rule cnf_or_pos :args (@t316)) % 1.12/1.30 (step @p593 :rule reordering :premises (@p592) :args ((or @t310 @t305 @t315 @t317))) % 1.12/1.30 (step @p594 :rule chain_m_resolution :premises (@p593 @p591 @p585 @p578) :args (@t317 (@list false false true) (@list @t309 @t304 @t315))) % 1.12/1.30 (step @p595 :rule beta-reduce :args ((= @t321 @t315))) % 1.12/1.30 (step @p596 :rule beta-reduce :args ((= @t322 @t302))) % 1.12/1.30 (step @p597 :rule beta-reduce :args ((= @t323 @t303))) % 1.12/1.30 (step @p598 :rule cong :premises (@p597) :args (@t324)) % 1.12/1.30 (step @p599 :rule nary_cong :premises (@p598 @p596) :args (@t325)) % 1.12/1.30 (step @p600 :rule cong :premises (@p599) :args (@t326)) % 1.12/1.30 (step @p601 :rule cong :premises (@p600) :args (@t327)) % 1.12/1.30 (step @p602 :rule beta-reduce :args ((= @t328 @t306))) % 1.12/1.30 (step @p603 :rule beta-reduce :args ((= @t329 @t307))) % 1.12/1.30 (step @p604 :rule beta-reduce :args ((= @t330 @t308))) % 1.12/1.30 (step @p605 :rule cong :premises (@p604) :args (@t331)) % 1.12/1.30 (step @p606 :rule nary_cong :premises (@p605 @p603) :args (@t332)) % 1.12/1.30 (step @p607 :rule cong :premises (@p606) :args (@t333)) % 1.12/1.30 (step @p608 :rule cong :premises (@p607) :args (@t334)) % 1.12/1.30 (step @p609 :rule nary_cong :premises (@p154 @p608 @p602) :args (@t335)) % 1.12/1.30 (step @p610 :rule cong :premises (@p609) :args (@t336)) % 1.12/1.30 (step @p611 :rule cong :premises (@p610) :args (@t337)) % 1.12/1.30 (step @p612 :rule nary_cong :premises (@p611 @p601 @p595) :args (@t338)) % 1.12/1.30 (step @p613 :rule refl :args (@t175)) % 1.12/1.30 (step @p614 :rule cong :premises (@p613 @p612) :args ((=> @t175 @t338))) % 1.12/1.30 (assume-push @p622 @t175) % 1.12/1.30 (step @p616 :rule instantiate :premises (@p565) :args ((@list @t320 @t298))) % 1.12/1.30 (step-pop @p623 :rule scope :premises (@p616)) % 1.12/1.30 (step @p617 :rule process_scope :premises (@p623) :args (@t338)) % 1.12/1.30 (step @p619 :rule eq_resolve :premises (@p617 @p614)) % 1.12/1.30 (step @p620 :rule implies_elim :premises (@p619)) % 1.12/1.30 (step @p621 false :rule chain_m_resolution :premises (@p620 @p594 @p565) :args (false (@list true false) (@list @t316 @t175))) % 1.12/1.30 ) % 1.12/1.30 % SZS output end Proof % 1.12/1.30 % cvc5 exiting %------------------------------------------------------------------------------