%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG253^1 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:05:39 AM UTC 2026 % Result : Theorem 0.42s 0.87s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : ALG253^1 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n003.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 01:54:59 EDT 2026 % 0.16/0.36 % CPUTime : % 0.36/0.60 %----Proving TH0 % 0.42/0.87 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.42/0.87 % SZS status Theorem % 0.42/0.87 % SZS output start Proof % 0.42/0.87 ( % 0.42/0.87 (declare-sort tptp.term 0) % 0.42/0.87 (declare-sort tptp.subst 0) % 0.42/0.87 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.42/0.87 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.42/0.87 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.42/0.87 (declare-const tptp.one tptp.term) % 0.42/0.87 (declare-const tptp.sh tptp.subst) % 0.42/0.87 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.42/0.87 (declare-const tptp.var (-> tptp.term Bool)) % 0.42/0.87 (declare-const tptp.id tptp.subst) % 0.42/0.87 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3b Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3a Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3 Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem2 Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem1 Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasinduction_lem0 Bool) % 0.42/0.87 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasapnotvar Bool) % 0.42/0.87 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.42/0.87 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.42/0.87 (declare-const tptp.hoaslamnotvar Bool) % 0.42/0.87 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.42/0.87 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.42/0.87 (declare-const tptp.hoaslamnotap Bool) % 0.42/0.87 (declare-const tptp.hoaslaminj_lthm Bool) % 0.42/0.87 (declare-const tptp.hoaslaminj_gthm Bool) % 0.42/0.87 (declare-const tptp.hoaslaminj Bool) % 0.42/0.87 (declare-const tptp.hoasapinj2_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasapinj2_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasapinj2 Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.42/0.87 (declare-const tptp.axassoc Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.42/0.87 (declare-const tptp.axvarcons Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem0 Bool) % 0.42/0.87 (declare-const tptp.apinj1 Bool) % 0.42/0.87 (declare-const tptp.induction Bool) % 0.42/0.87 (declare-const tptp.apnotvar Bool) % 0.42/0.87 (declare-const tptp.laminj Bool) % 0.42/0.87 (declare-const tptp.axvarshift Bool) % 0.42/0.87 (declare-const tptp.ulamvarind Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.42/0.87 (declare-const tptp.ulamvarsh Bool) % 0.42/0.87 (declare-const tptp.ulamvar1 Bool) % 0.42/0.87 (declare-const tptp.axabs Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem1 Bool) % 0.42/0.87 (declare-const tptp.shinj Bool) % 0.42/0.87 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.42/0.87 (declare-const tptp.apinj2 Bool) % 0.42/0.87 (declare-const tptp.axvarid Bool) % 0.42/0.87 (declare-const tptp.axidl Bool) % 0.42/0.87 (declare-const tptp.axclos Bool) % 0.42/0.87 (declare-const tptp.termmset Bool) % 0.42/0.87 (declare-const tptp.axshiftcons Bool) % 0.42/0.87 (declare-const tptp.lamnotap Bool) % 0.42/0.87 (declare-const tptp.lamnotvar Bool) % 0.42/0.87 (declare-const tptp.axapp Bool) % 0.42/0.87 (declare-const tptp.axscons Bool) % 0.42/0.87 (declare-const tptp.axmap Bool) % 0.42/0.87 (declare-const tptp.axidr Bool) % 0.42/0.87 (declare-const tptp.induction2lem Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasapinj1_lthm Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem1v2 Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.42/0.87 (declare-const tptp.induction2 Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem2v2 Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem3v2 Bool) % 0.42/0.87 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.42/0.87 (declare-const tptp.pushprop Bool) % 0.42/0.87 (declare-const tptp.pushprop_gthm Bool) % 0.42/0.87 (declare-const tptp.hoasapinj1 Bool) % 0.42/0.87 (declare-const tptp.pushprop_lthm_orig Bool) % 0.42/0.87 (declare-const tptp.pushprop_lthm Bool) % 0.42/0.87 (declare-const tptp.induction2lem_gthm Bool) % 0.42/0.87 (declare-const tptp.induction2lem_lthm Bool) % 0.42/0.87 (declare-const tptp.induction2_gthm Bool) % 0.42/0.87 (declare-const tptp.induction2_lthm Bool) % 0.42/0.87 (declare-const tptp.substmonoid Bool) % 0.42/0.87 (declare-const tptp.substmonoid_gthm Bool) % 0.42/0.87 (declare-const tptp.termmset_gthm Bool) % 0.42/0.87 (declare-const tptp.substmonoid_lthm Bool) % 0.42/0.87 (declare-const tptp.termmset_lthm Bool) % 0.42/0.87 (declare-const tptp.hoasapinj1_gthm Bool) % 0.42/0.87 (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)))))))))))) % 0.42/0.87 (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)))))) % 0.42/0.87 (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))))) % 0.42/0.87 (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)))))) % 0.42/0.87 (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)))))))) % 0.42/0.87 (define @t1 () (@var "M" tptp.subst)) % 0.42/0.87 (define @t2 () (@var "B" tptp.term)) % 0.42/0.87 (define @t3 () (_ tptp.sub @t2)) % 0.42/0.87 (define @t4 () (_ @t3 @t1)) % 0.42/0.87 (define @t5 () (@var "A" tptp.term)) % 0.42/0.87 (define @t6 () (_ tptp.sub @t5)) % 0.42/0.87 (define @t7 () (_ @t6 @t1)) % 0.42/0.87 (define @t8 () (_ (_ tptp.ap @t7) @t4)) % 0.42/0.87 (define @t9 () (_ tptp.ap @t5)) % 0.42/0.87 (define @t10 () (_ @t9 @t2)) % 0.42/0.87 (define @t11 () (_ (_ tptp.sub @t10) @t1)) % 0.42/0.87 (define @t12 () (= @t11 @t8)) % 0.42/0.87 (define @t13 () (@list @t5 @t2 @t1)) % 0.42/0.87 (define @t14 () (forall @t13 @t12)) % 0.42/0.87 (define @t15 () (= tptp.axapp @t14)) % 0.42/0.87 (define @t16 () (_ (_ tptp.push @t5) @t1)) % 0.42/0.87 (define @t17 () (_ tptp.sub tptp.one)) % 0.42/0.87 (define @t18 () (_ @t17 @t16)) % 0.42/0.87 (define @t19 () (@list @t5 @t1)) % 0.42/0.87 (define @t20 () (forall @t19 (= @t18 @t5))) % 0.42/0.87 (define @t21 () (= tptp.axvarcons @t20)) % 0.42/0.87 (define @t22 () (_ @t6 tptp.id)) % 0.42/0.87 (define @t23 () (@list @t5)) % 0.42/0.87 (define @t24 () (forall @t23 (= @t22 @t5))) % 0.42/0.87 (define @t25 () (= tptp.axvarid @t24)) % 0.42/0.87 (define @t26 () (_ tptp.comp @t1)) % 0.42/0.87 (define @t27 () (_ @t26 tptp.sh)) % 0.42/0.87 (define @t28 () (_ tptp.push tptp.one)) % 0.42/0.87 (define @t29 () (_ @t28 @t27)) % 0.42/0.87 (define @t30 () (_ @t6 @t29)) % 0.42/0.87 (define @t31 () (_ tptp.lam @t30)) % 0.42/0.87 (define @t32 () (_ tptp.lam @t5)) % 0.42/0.87 (define @t33 () (_ (_ tptp.sub @t32) @t1)) % 0.42/0.87 (define @t34 () (= @t33 @t31)) % 0.42/0.87 (define @t35 () (forall @t19 @t34)) % 0.42/0.87 (define @t36 () (= tptp.axabs @t35)) % 0.42/0.87 (define @t37 () (@var "N" tptp.subst)) % 0.42/0.87 (define @t38 () (_ @t26 @t37)) % 0.42/0.87 (define @t39 () (_ @t6 @t38)) % 0.42/0.87 (define @t40 () (_ (_ tptp.sub @t7) @t37)) % 0.42/0.87 (define @t41 () (= @t40 @t39)) % 0.42/0.87 (define @t42 () (@list @t5 @t1 @t37)) % 0.42/0.87 (define @t43 () (forall @t42 @t41)) % 0.42/0.87 (define @t44 () (= tptp.axclos @t43)) % 0.42/0.87 (define @t45 () (_ (_ tptp.comp tptp.id) @t1)) % 0.42/0.87 (define @t46 () (@list @t1)) % 0.42/0.87 (define @t47 () (forall @t46 (= @t45 @t1))) % 0.42/0.87 (define @t48 () (= tptp.axidl @t47)) % 0.42/0.87 (define @t49 () (_ tptp.comp tptp.sh)) % 0.42/0.87 (define @t50 () (_ @t49 @t16)) % 0.42/0.87 (define @t51 () (forall @t19 (= @t50 @t1))) % 0.42/0.87 (define @t52 () (= tptp.axshiftcons @t51)) % 0.42/0.87 (define @t53 () (@var "K" tptp.subst)) % 0.42/0.87 (define @t54 () (_ (_ tptp.comp @t37) @t53)) % 0.42/0.87 (define @t55 () (_ @t26 @t54)) % 0.42/0.87 (define @t56 () (_ (_ tptp.comp @t38) @t53)) % 0.42/0.87 (define @t57 () (= @t56 @t55)) % 0.42/0.87 (define @t58 () (@list @t1 @t37 @t53)) % 0.42/0.87 (define @t59 () (forall @t58 @t57)) % 0.42/0.87 (define @t60 () (= tptp.axassoc @t59)) % 0.42/0.87 (define @t61 () (_ @t6 @t37)) % 0.42/0.87 (define @t62 () (_ (_ tptp.push @t61) @t38)) % 0.42/0.87 (define @t63 () (_ (_ tptp.comp @t16) @t37)) % 0.42/0.87 (define @t64 () (= @t63 @t62)) % 0.42/0.87 (define @t65 () (forall @t42 @t64)) % 0.42/0.87 (define @t66 () (= tptp.axmap @t65)) % 0.42/0.87 (define @t67 () (_ @t26 tptp.id)) % 0.42/0.87 (define @t68 () (forall @t46 (= @t67 @t1))) % 0.42/0.87 (define @t69 () (= tptp.axidr @t68)) % 0.42/0.87 (define @t70 () (_ @t28 tptp.sh)) % 0.42/0.87 (define @t71 () (= tptp.axvarshift (= @t70 tptp.id))) % 0.42/0.87 (define @t72 () (_ @t49 @t1)) % 0.42/0.87 (define @t73 () (_ @t17 @t1)) % 0.42/0.87 (define @t74 () (_ (_ tptp.push @t73) @t72)) % 0.42/0.87 (define @t75 () (forall @t46 (= @t74 @t1))) % 0.42/0.87 (define @t76 () (= tptp.axscons @t75)) % 0.42/0.87 (define @t77 () (_ tptp.var tptp.one)) % 0.42/0.87 (define @t78 () (_ @t6 tptp.sh)) % 0.42/0.87 (define @t79 () (_ tptp.var @t78)) % 0.42/0.87 (define @t80 () (_ tptp.var @t5)) % 0.42/0.87 (define @t81 () (forall @t23 (=> @t80 @t79))) % 0.42/0.87 (define @t82 () (= tptp.ulamvarsh @t81)) % 0.42/0.87 (define @t83 () (@var "P" (-> tptp.term Bool))) % 0.42/0.87 (define @t84 () (_ @t83 @t5)) % 0.42/0.87 (define @t85 () (forall @t23 (=> @t80 @t84))) % 0.42/0.87 (define @t86 () (_ @t83 @t78)) % 0.42/0.87 (define @t87 () (=> @t84 @t86)) % 0.42/0.87 (define @t88 () (forall @t23 (=> @t80 @t87))) % 0.42/0.87 (define @t89 () (=> @t88 @t85)) % 0.42/0.87 (define @t90 () (_ @t83 tptp.one)) % 0.42/0.87 (define @t91 () (=> @t90 @t89)) % 0.42/0.87 (define @t92 () (@list @t83)) % 0.42/0.87 (define @t93 () (forall @t92 @t91)) % 0.42/0.87 (define @t94 () (= tptp.ulamvarind @t93)) % 0.42/0.87 (define @t95 () (= @t5 @t2)) % 0.42/0.87 (define @t96 () (@var "D" tptp.term)) % 0.42/0.87 (define @t97 () (_ tptp.ap @t2)) % 0.42/0.87 (define @t98 () (_ @t97 @t96)) % 0.42/0.87 (define @t99 () (@var "C" tptp.term)) % 0.42/0.87 (define @t100 () (_ @t9 @t99)) % 0.42/0.87 (define @t101 () (= @t100 @t98)) % 0.42/0.87 (define @t102 () (@list @t5 @t2 @t99 @t96)) % 0.42/0.87 (define @t103 () (forall @t102 (=> @t101 @t95))) % 0.42/0.87 (define @t104 () (= tptp.apinj1 @t103)) % 0.42/0.87 (define @t105 () (= @t99 @t96)) % 0.42/0.87 (define @t106 () (forall @t102 (=> @t101 @t105))) % 0.42/0.87 (define @t107 () (= tptp.apinj2 @t106)) % 0.42/0.87 (define @t108 () (_ tptp.lam @t2)) % 0.42/0.87 (define @t109 () (= @t32 @t108)) % 0.42/0.87 (define @t110 () (@list @t5 @t2)) % 0.42/0.87 (define @t111 () (forall @t110 (=> @t109 @t95))) % 0.42/0.87 (define @t112 () (= tptp.laminj @t111)) % 0.42/0.87 (define @t113 () (_ @t3 tptp.sh)) % 0.42/0.87 (define @t114 () (= @t78 @t113)) % 0.42/0.87 (define @t115 () (forall @t110 (=> @t114 @t95))) % 0.42/0.87 (define @t116 () (= tptp.shinj @t115)) % 0.42/0.87 (define @t117 () (_ @t97 @t99)) % 0.42/0.87 (define @t118 () (= @t32 @t117)) % 0.42/0.87 (define @t119 () (not @t118)) % 0.42/0.87 (define @t120 () (@list @t5 @t2 @t99)) % 0.42/0.87 (define @t121 () (forall @t120 @t119)) % 0.42/0.87 (define @t122 () (= tptp.lamnotap @t121)) % 0.42/0.87 (define @t123 () (_ tptp.var @t10)) % 0.42/0.87 (define @t124 () (not @t123)) % 0.42/0.87 (define @t125 () (forall @t110 @t124)) % 0.42/0.87 (define @t126 () (= tptp.apnotvar @t125)) % 0.42/0.87 (define @t127 () (_ tptp.var @t32)) % 0.42/0.87 (define @t128 () (not @t127)) % 0.42/0.87 (define @t129 () (forall @t23 @t128)) % 0.42/0.87 (define @t130 () (= tptp.lamnotvar @t129)) % 0.42/0.87 (define @t131 () (forall @t23 @t84)) % 0.42/0.87 (define @t132 () (_ @t83 @t32)) % 0.42/0.87 (define @t133 () (forall @t23 (=> @t84 @t132))) % 0.42/0.87 (define @t134 () (=> @t133 @t131)) % 0.42/0.87 (define @t135 () (_ @t83 @t10)) % 0.42/0.87 (define @t136 () (_ @t83 @t2)) % 0.42/0.87 (define @t137 () (=> @t136 @t135)) % 0.42/0.87 (define @t138 () (forall @t110 (=> @t84 @t137))) % 0.42/0.87 (define @t139 () (=> @t138 @t134)) % 0.42/0.87 (define @t140 () (=> @t85 @t139)) % 0.42/0.87 (define @t141 () (forall @t92 @t140)) % 0.42/0.87 (define @t142 () (= tptp.induction @t141)) % 0.42/0.87 (define @t143 () (@var "Q" (-> tptp.term Bool))) % 0.42/0.87 (define @t144 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t83) @t143)) % 0.42/0.87 (define @t145 () (@list @t143)) % 0.42/0.87 (define @t146 () (@list @t83 @t5 @t1)) % 0.42/0.87 (define @t147 () (_ tptp.push @t2)) % 0.42/0.87 (define @t148 () (@var "K" (-> tptp.term Bool))) % 0.42/0.87 (define @t149 () (@list @t83 @t143 @t5 @t1)) % 0.42/0.87 (define @t150 () (_ tptp.sub @t99)) % 0.42/0.87 (define @t151 () (@list @t99)) % 0.42/0.87 (define @t152 () (_ @t83 @t4)) % 0.42/0.87 (define @t153 () (_ tptp.var @t2)) % 0.42/0.87 (define @t154 () (@list @t2)) % 0.42/0.87 (define @t155 () (forall @t154 (=> @t153 @t152))) % 0.42/0.87 (define @t156 () (_ @t3 @t16)) % 0.42/0.87 (define @t157 () (_ @t83 @t156)) % 0.42/0.87 (define @t158 () (forall @t154 (=> @t153 @t157))) % 0.42/0.87 (define @t159 () (_ @t143 @t2)) % 0.42/0.87 (define @t160 () (=> @t84 @t158)) % 0.42/0.87 (define @t161 () (=> @t155 @t160)) % 0.42/0.87 (define @t162 () (forall @t146 @t161)) % 0.42/0.87 (define @t163 () (= tptp.pushprop @t162)) % 0.42/0.87 (define @t164 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.42/0.87 (define @t165 () (_ @t83 @t7)) % 0.42/0.87 (define @t166 () (=> @t155 @t165)) % 0.42/0.87 (define @t167 () (forall @t19 @t166)) % 0.42/0.87 (define @t168 () (_ @t147 tptp.id)) % 0.42/0.87 (define @t169 () (_ @t6 @t168)) % 0.42/0.87 (define @t170 () (_ @t83 @t169)) % 0.42/0.87 (define @t171 () (forall @t154 (=> @t136 @t170))) % 0.42/0.87 (define @t172 () (=> @t171 @t132)) % 0.42/0.87 (define @t173 () (forall @t23 @t172)) % 0.42/0.87 (define @t174 () (=> @t173 @t167)) % 0.42/0.87 (define @t175 () (=> @t138 @t174)) % 0.42/0.87 (define @t176 () (forall @t92 @t175)) % 0.42/0.87 (define @t177 () (= tptp.induction2lem @t176)) % 0.42/0.87 (define @t178 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.42/0.87 (define @t179 () (=> @t173 @t131)) % 0.42/0.87 (define @t180 () (=> @t138 @t179)) % 0.42/0.87 (define @t181 () (=> @t85 @t180)) % 0.42/0.87 (define @t182 () (forall @t92 @t181)) % 0.42/0.87 (define @t183 () (= tptp.induction2 @t182)) % 0.42/0.87 (define @t184 () (=> tptp.induction2lem tptp.induction2)) % 0.42/0.87 (define @t185 () (=> tptp.pushprop @t184)) % 0.42/0.87 (define @t186 () (=> tptp.induction @t185)) % 0.42/0.87 (define @t187 () (=> tptp.lamnotvar @t186)) % 0.42/0.87 (define @t188 () (=> tptp.apnotvar @t187)) % 0.42/0.87 (define @t189 () (=> tptp.lamnotap @t188)) % 0.42/0.87 (define @t190 () (=> tptp.shinj @t189)) % 0.42/0.87 (define @t191 () (=> tptp.laminj @t190)) % 0.42/0.87 (define @t192 () (=> tptp.apinj2 @t191)) % 0.42/0.87 (define @t193 () (=> tptp.apinj1 @t192)) % 0.42/0.87 (define @t194 () (=> tptp.ulamvarind @t193)) % 0.42/0.87 (define @t195 () (=> tptp.ulamvarsh @t194)) % 0.42/0.87 (define @t196 () (=> tptp.ulamvar1 @t195)) % 0.42/0.87 (define @t197 () (=> tptp.axscons @t196)) % 0.42/0.87 (define @t198 () (=> tptp.axvarshift @t197)) % 0.42/0.87 (define @t199 () (=> tptp.axidr @t198)) % 0.42/0.87 (define @t200 () (=> tptp.axmap @t199)) % 0.42/0.87 (define @t201 () (=> tptp.axassoc @t200)) % 0.42/0.87 (define @t202 () (=> tptp.axshiftcons @t201)) % 0.42/0.87 (define @t203 () (=> tptp.axidl @t202)) % 0.42/0.87 (define @t204 () (=> tptp.axclos @t203)) % 0.42/0.87 (define @t205 () (=> tptp.axabs @t204)) % 0.42/0.87 (define @t206 () (=> tptp.axvarid @t205)) % 0.42/0.87 (define @t207 () (=> tptp.axvarcons @t206)) % 0.42/0.87 (define @t208 () (=> tptp.axapp @t207)) % 0.42/0.87 (define @t209 () (= tptp.induction2_gthm @t208)) % 0.42/0.87 (define @t210 () (_ tptp.hoasap tptp.id)) % 0.42/0.87 (define @t211 () (_ (_ @t210 @t5) tptp.id)) % 0.42/0.87 (define @t212 () (= (_ @t211 @t99) (_ (_ (_ @t210 @t2) tptp.id) @t96))) % 0.42/0.87 (define @t213 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.42/0.87 (define @t214 () (_ (_ @t213 @t1) @t5)) % 0.42/0.87 (define @t215 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.42/0.87 (define @t216 () (_ @t215 @t1)) % 0.42/0.87 (define @t217 () (_ @t216 @t5)) % 0.42/0.87 (define @t218 () (@list @t1 @t5)) % 0.42/0.87 (define @t219 () (_ tptp.hoaslam tptp.id)) % 0.42/0.87 (define @t220 () (_ @t219 (lambda @t218 @t217))) % 0.42/0.87 (define @t221 () (@list @t1 @t5 @t37)) % 0.42/0.87 (define @t222 () (_ (_ @t215 @t38) @t61)) % 0.42/0.87 (define @t223 () (_ (_ tptp.sub @t217) @t37)) % 0.42/0.87 (define @t224 () (forall @t221 (= @t223 @t222))) % 0.42/0.87 (define @t225 () (@list @t215)) % 0.42/0.87 (define @t226 () (_ @t211 @t2)) % 0.42/0.87 (define @t227 () (_ tptp.hoasvar tptp.id)) % 0.42/0.87 (define @t228 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.42/0.87 (define @t229 () (_ (_ tptp.hoasinduction_p_and_p_prime @t228) @t143)) % 0.42/0.87 (define @t230 () (@list @t228)) % 0.42/0.87 (define @t231 () (_ @t143 @t5)) % 0.42/0.87 (define @t232 () (_ @t228 tptp.id)) % 0.42/0.87 (define @t233 () (_ (_ @t232 @t5) tptp.id)) % 0.42/0.87 (define @t234 () (forall @t23 (=> (_ (_ @t227 @t5) tptp.id) @t233))) % 0.42/0.87 (define @t235 () (_ (_ (_ @t228 @t1) @t5) (_ (_ tptp.comp @t53) @t37))) % 0.42/0.87 (define @t236 () (_ (_ (_ @t228 (_ @t26 @t53)) (_ @t6 @t53)) @t37)) % 0.42/0.87 (define @t237 () (@list @t1 @t5 @t37 @t53)) % 0.42/0.87 (define @t238 () (forall @t237 (=> @t236 @t235))) % 0.42/0.87 (define @t239 () (forall @t237 (=> @t235 @t236))) % 0.42/0.87 (define @t240 () (@list @t228 @t143)) % 0.42/0.87 (define @t241 () (_ (_ @t232 @t2) tptp.id)) % 0.42/0.87 (define @t242 () (forall @t110 (=> @t233 (=> @t241 (_ (_ @t232 @t226) tptp.id))))) % 0.42/0.87 (define @t243 () (=> (forall @t23 (=> @t233 (_ (_ @t232 (_ (_ @t215 tptp.id) @t5)) tptp.id))) (_ (_ @t232 @t220) tptp.id))) % 0.42/0.87 (define @t244 () (forall @t225 (=> @t224 @t243))) % 0.42/0.87 (define @t245 () (=> @t244 (=> @t229 (forall @t23 (=> (forall @t154 (=> @t159 (_ @t143 @t169))) (_ @t143 @t32)))))) % 0.42/0.87 (define @t246 () (=> 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))))))))))))))))))))))))))))))))))) % 0.42/0.87 (define @t247 () (=> 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))))))))))))))))))))))))))))))))))) % 0.42/0.87 (define @t248 () (forall @t154 (=> @t241 (_ (_ @t232 @t169) tptp.id)))) % 0.42/0.87 (define @t249 () (forall @t23 (=> @t248 (_ (_ @t232 (_ tptp.lam (_ @t6 @t70))) tptp.id)))) % 0.42/0.87 (define @t250 () (=> @t244 (forall @t23 (=> @t248 (_ (_ @t232 @t32) tptp.id))))) % 0.42/0.87 (define @t251 () (_ (_ @t215 tptp.sh) tptp.one)) % 0.42/0.87 (define @t252 () (=> @t242 (=> @t244 (forall @t23 @t233)))) % 0.42/0.87 (define @t253 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.42/0.87 (define @t254 () (not tptp.induction2_gthm)) % 0.42/0.87 (define @t255 () (@var "X" tptp.term)) % 0.42/0.87 (define @t256 () (_ @t143 @t255)) % 0.42/0.87 (define @t257 () (@list @t255)) % 0.42/0.87 (define @t258 () (lambda (@list @t5 @t1 @t83 @t143) (forall @t257 (= @t256 (_ @t83 (_ (_ tptp.sub @t255) @t16)))))) % 0.42/0.87 (define @t259 () (lambda (@list @t1 @t5 @t37 @t2) (_ (_ tptp.ap @t61) @t2))) % 0.42/0.87 (define @t260 () (lambda (@list @t1 @t215) (_ tptp.lam @t251))) % 0.42/0.87 (define @t261 () (lambda @t221 (_ tptp.var @t61))) % 0.42/0.87 (define @t262 () (lambda @t240 (forall @t257 (= @t256 (_ (_ @t232 @t255) tptp.id))))) % 0.42/0.87 (define @t263 () (@var "BOUND_VARIABLE_9396" tptp.term)) % 0.42/0.87 (define @t264 () (_ @t83 @t263)) % 0.42/0.87 (define @t265 () (tptp.lam @t5)) % 0.42/0.87 (define @t266 () (_ @t83 @t265)) % 0.42/0.87 (define @t267 () (tptp.push tptp.one tptp.sh)) % 0.42/0.87 (define @t268 () (tptp.push @t2 @t267)) % 0.42/0.87 (define @t269 () (tptp.sub @t5 @t268)) % 0.42/0.87 (define @t270 () (_ @t83 @t2)) % 0.42/0.87 (define @t271 () (not @t270)) % 0.42/0.87 (define @t272 () (not (forall @t23 (or (not (forall @t154 (or @t271 (_ @t83 @t269)))) @t266)))) % 0.42/0.87 (define @t273 () (tptp.ap @t5 @t2)) % 0.42/0.87 (define @t274 () (_ @t83 @t273)) % 0.42/0.87 (define @t275 () (_ @t83 @t5)) % 0.42/0.87 (define @t276 () (not @t275)) % 0.42/0.87 (define @t277 () (forall @t110 (or @t276 @t271 @t274))) % 0.42/0.87 (define @t278 () (not @t277)) % 0.42/0.87 (define @t279 () (tptp.var @t5)) % 0.42/0.87 (define @t280 () (not @t279)) % 0.42/0.87 (define @t281 () (forall @t23 (or @t280 @t275))) % 0.42/0.87 (define @t282 () (not @t281)) % 0.42/0.87 (define @t283 () (@list @t83 @t263)) % 0.42/0.87 (define @t284 () (forall @t283 (or @t282 @t278 @t272 @t264))) % 0.42/0.87 (define @t285 () (@var "BOUND_VARIABLE_9371" tptp.subst)) % 0.42/0.87 (define @t286 () (@var "BOUND_VARIABLE_9369" tptp.term)) % 0.42/0.87 (define @t287 () (_ @t83 (tptp.sub @t286 @t285))) % 0.42/0.87 (define @t288 () (tptp.var @t2)) % 0.42/0.87 (define @t289 () (not @t288)) % 0.42/0.87 (define @t290 () (not (forall @t154 (or @t289 (_ @t83 (tptp.sub @t2 @t285)))))) % 0.42/0.87 (define @t291 () (@list @t83 @t286 @t285)) % 0.42/0.87 (define @t292 () (tptp.push @t5 @t1)) % 0.42/0.87 (define @t293 () (@var "BOUND_VARIABLE_9324" tptp.term)) % 0.42/0.87 (define @t294 () (_ @t83 (tptp.sub @t293 @t292))) % 0.42/0.87 (define @t295 () (not (tptp.var @t293))) % 0.42/0.87 (define @t296 () (tptp.sub @t2 @t1)) % 0.42/0.87 (define @t297 () (_ @t83 @t296)) % 0.42/0.87 (define @t298 () (forall @t154 (or @t289 @t297))) % 0.42/0.87 (define @t299 () (not @t298)) % 0.42/0.87 (define @t300 () (or @t299 @t276 @t295 @t294)) % 0.42/0.87 (define @t301 () (@list @t83 @t5 @t1 @t293)) % 0.42/0.87 (define @t302 () (forall @t301 @t300)) % 0.42/0.87 (define @t303 () (@var "BOUND_VARIABLE_9170" tptp.term)) % 0.42/0.87 (define @t304 () (_ @t83 @t303)) % 0.42/0.87 (define @t305 () (forall @t23 (or @t276 @t266))) % 0.42/0.87 (define @t306 () (not @t305)) % 0.42/0.87 (define @t307 () (or @t282 @t278 @t306 @t304)) % 0.42/0.87 (define @t308 () (forall (@list @t83 @t303) @t307)) % 0.42/0.87 (define @t309 () (tptp.var @t265)) % 0.42/0.87 (define @t310 () (forall @t23 (not @t309))) % 0.42/0.87 (define @t311 () (tptp.var @t273)) % 0.42/0.87 (define @t312 () (forall @t110 (not @t311))) % 0.42/0.87 (define @t313 () (tptp.ap @t2 @t99)) % 0.42/0.87 (define @t314 () (forall @t120 (not (= @t265 @t313)))) % 0.42/0.87 (define @t315 () (tptp.sub @t2 tptp.sh)) % 0.42/0.87 (define @t316 () (tptp.sub @t5 tptp.sh)) % 0.42/0.87 (define @t317 () (forall @t110 (or (not (= @t316 @t315)) @t95))) % 0.42/0.87 (define @t318 () (tptp.lam @t2)) % 0.42/0.87 (define @t319 () (forall @t110 (or (not (= @t265 @t318)) @t95))) % 0.42/0.87 (define @t320 () (tptp.ap @t2 @t96)) % 0.42/0.87 (define @t321 () (tptp.ap @t5 @t99)) % 0.42/0.87 (define @t322 () (not (= @t321 @t320))) % 0.42/0.87 (define @t323 () (forall @t102 (or @t322 @t105))) % 0.42/0.87 (define @t324 () (forall @t102 (or @t322 @t95))) % 0.42/0.87 (define @t325 () (@var "BOUND_VARIABLE_9074" tptp.term)) % 0.42/0.87 (define @t326 () (_ @t83 @t325)) % 0.42/0.87 (define @t327 () (not (tptp.var @t325))) % 0.42/0.87 (define @t328 () (_ @t83 @t316)) % 0.42/0.87 (define @t329 () (forall @t23 (or @t280 @t276 @t328))) % 0.42/0.87 (define @t330 () (not @t329)) % 0.42/0.87 (define @t331 () (_ @t83 tptp.one)) % 0.42/0.87 (define @t332 () (not @t331)) % 0.42/0.87 (define @t333 () (or @t332 @t330 @t327 @t326)) % 0.42/0.87 (define @t334 () (@list @t83 @t325)) % 0.42/0.87 (define @t335 () (forall @t334 @t333)) % 0.42/0.87 (define @t336 () (tptp.var @t316)) % 0.42/0.87 (define @t337 () (forall @t23 (or @t280 @t336))) % 0.42/0.87 (define @t338 () (=> @t337 (=> @t335 (=> @t324 (=> @t323 (=> @t319 (=> @t317 (=> @t314 (=> @t312 (=> @t310 (=> @t308 (=> @t302 (=> (forall @t291 (or @t278 @t272 @t290 @t287)) @t284))))))))))))) % 0.42/0.87 (define @t339 () (tptp.var tptp.one)) % 0.42/0.87 (define @t340 () (=> @t77 @t338)) % 0.42/0.87 (define @t341 () (tptp.comp tptp.sh @t1)) % 0.42/0.87 (define @t342 () (tptp.sub tptp.one @t1)) % 0.42/0.87 (define @t343 () (tptp.push @t342 @t341)) % 0.42/0.87 (define @t344 () (forall @t46 (= @t1 @t343))) % 0.42/0.87 (define @t345 () (=> @t344 @t340)) % 0.42/0.87 (define @t346 () (forall @t46 (= @t1 (tptp.comp @t1 @t267)))) % 0.42/0.87 (define @t347 () (=> @t346 @t345)) % 0.42/0.87 (define @t348 () (tptp.comp @t1 @t37)) % 0.42/0.87 (define @t349 () (tptp.sub @t5 @t37)) % 0.42/0.87 (define @t350 () (tptp.push @t349 @t348)) % 0.42/0.87 (define @t351 () (tptp.comp @t292 @t37)) % 0.42/0.87 (define @t352 () (forall @t42 (= @t351 @t350))) % 0.42/0.87 (define @t353 () (=> @t352 @t347)) % 0.42/0.87 (define @t354 () (tptp.comp @t37 @t53)) % 0.42/0.87 (define @t355 () (tptp.comp @t1 @t354)) % 0.42/0.87 (define @t356 () (tptp.comp @t348 @t53)) % 0.42/0.87 (define @t357 () (forall @t58 (= @t356 @t355))) % 0.42/0.87 (define @t358 () (=> @t357 @t353)) % 0.42/0.87 (define @t359 () (tptp.comp tptp.sh @t292)) % 0.42/0.87 (define @t360 () (forall @t19 (= @t1 @t359))) % 0.42/0.87 (define @t361 () (=> @t360 @t358)) % 0.42/0.87 (define @t362 () (forall @t46 (= @t1 (tptp.comp @t267 @t1)))) % 0.42/0.87 (define @t363 () (=> @t362 @t361)) % 0.42/0.87 (define @t364 () (tptp.sub @t5 @t348)) % 0.42/0.87 (define @t365 () (tptp.sub @t5 @t1)) % 0.42/0.87 (define @t366 () (tptp.sub @t365 @t37)) % 0.42/0.87 (define @t367 () (forall @t42 (= @t366 @t364))) % 0.42/0.87 (define @t368 () (=> @t367 @t363)) % 0.42/0.87 (define @t369 () (tptp.comp @t1 tptp.sh)) % 0.42/0.87 (define @t370 () (tptp.push tptp.one @t369)) % 0.42/0.87 (define @t371 () (tptp.sub @t5 @t370)) % 0.42/0.87 (define @t372 () (tptp.lam @t371)) % 0.42/0.87 (define @t373 () (tptp.sub @t265 @t1)) % 0.42/0.87 (define @t374 () (forall @t19 (= @t373 @t372))) % 0.42/0.87 (define @t375 () (=> @t374 @t368)) % 0.42/0.87 (define @t376 () (forall @t23 (= @t5 (tptp.sub @t5 @t267)))) % 0.42/0.87 (define @t377 () (=> @t376 @t375)) % 0.42/0.87 (define @t378 () (tptp.sub tptp.one @t292)) % 0.42/0.87 (define @t379 () (forall @t19 (= @t5 @t378))) % 0.42/0.87 (define @t380 () (=> @t379 @t377)) % 0.42/0.87 (define @t381 () (tptp.ap @t365 @t296)) % 0.42/0.87 (define @t382 () (tptp.sub @t273 @t1)) % 0.42/0.87 (define @t383 () (forall @t13 (= @t382 @t381))) % 0.42/0.87 (define @t384 () (=> @t383 @t380)) % 0.42/0.87 (define @t385 () (tptp.push @t2 @t70)) % 0.42/0.87 (define @t386 () (tptp.sub @t5 @t385)) % 0.42/0.87 (define @t387 () (_ @t83 @t386)) % 0.42/0.87 (define @t388 () (or @t271 @t387)) % 0.42/0.87 (define @t389 () (forall @t154 @t388)) % 0.42/0.87 (define @t390 () (not @t389)) % 0.42/0.87 (define @t391 () (or @t390 @t266)) % 0.42/0.87 (define @t392 () (forall @t23 @t391)) % 0.42/0.87 (define @t393 () (not @t392)) % 0.42/0.87 (define @t394 () (or @t282 @t278 @t393 @t264)) % 0.42/0.87 (define @t395 () (forall @t283 @t394)) % 0.42/0.87 (define @t396 () (or @t278 @t393 @t290 @t287)) % 0.42/0.87 (define @t397 () (forall @t291 @t396)) % 0.42/0.87 (define @t398 () (=> @t397 @t395)) % 0.42/0.87 (define @t399 () (=> @t302 @t398)) % 0.42/0.87 (define @t400 () (=> @t308 @t399)) % 0.42/0.87 (define @t401 () (=> @t310 @t400)) % 0.42/0.87 (define @t402 () (=> @t312 @t401)) % 0.42/0.87 (define @t403 () (=> @t314 @t402)) % 0.42/0.87 (define @t404 () (=> @t317 @t403)) % 0.42/0.87 (define @t405 () (=> @t319 @t404)) % 0.42/0.87 (define @t406 () (=> @t323 @t405)) % 0.42/0.87 (define @t407 () (=> @t324 @t406)) % 0.42/0.87 (define @t408 () (=> @t335 @t407)) % 0.42/0.87 (define @t409 () (=> @t337 @t408)) % 0.42/0.87 (define @t410 () (=> @t77 @t409)) % 0.42/0.87 (define @t411 () (=> @t344 @t410)) % 0.42/0.87 (define @t412 () (=> (= @t70 @t70) @t411)) % 0.42/0.87 (define @t413 () (tptp.comp @t1 @t70)) % 0.42/0.87 (define @t414 () (= @t1 @t413)) % 0.42/0.87 (define @t415 () (forall @t46 @t414)) % 0.42/0.87 (define @t416 () (=> @t415 @t412)) % 0.42/0.87 (define @t417 () (=> @t352 @t416)) % 0.42/0.87 (define @t418 () (=> @t357 @t417)) % 0.42/0.87 (define @t419 () (=> @t360 @t418)) % 0.42/0.87 (define @t420 () (tptp.comp @t70 @t1)) % 0.42/0.87 (define @t421 () (= @t1 @t420)) % 0.42/0.87 (define @t422 () (forall @t46 @t421)) % 0.42/0.87 (define @t423 () (=> @t422 @t419)) % 0.42/0.87 (define @t424 () (=> @t367 @t423)) % 0.42/0.87 (define @t425 () (=> @t374 @t424)) % 0.42/0.87 (define @t426 () (tptp.sub @t5 @t70)) % 0.42/0.87 (define @t427 () (= @t5 @t426)) % 0.42/0.87 (define @t428 () (forall @t23 @t427)) % 0.42/0.87 (define @t429 () (=> @t428 @t425)) % 0.42/0.87 (define @t430 () (=> @t379 @t429)) % 0.42/0.87 (define @t431 () (=> @t383 @t430)) % 0.42/0.87 (define @t432 () (tptp.push @t2 tptp.id)) % 0.42/0.87 (define @t433 () (tptp.sub @t5 @t432)) % 0.42/0.87 (define @t434 () (_ @t83 @t433)) % 0.42/0.87 (define @t435 () (or @t271 @t434)) % 0.42/0.87 (define @t436 () (forall @t154 @t435)) % 0.42/0.87 (define @t437 () (not @t436)) % 0.42/0.87 (define @t438 () (or @t437 @t266)) % 0.42/0.87 (define @t439 () (forall @t23 @t438)) % 0.42/0.87 (define @t440 () (not @t439)) % 0.42/0.87 (define @t441 () (or @t282 @t278 @t440 @t264)) % 0.42/0.87 (define @t442 () (forall @t283 @t441)) % 0.42/0.87 (define @t443 () (or @t278 @t440 @t290 @t287)) % 0.42/0.87 (define @t444 () (forall @t291 @t443)) % 0.42/0.87 (define @t445 () (=> @t444 @t442)) % 0.42/0.87 (define @t446 () (=> @t302 @t445)) % 0.42/0.87 (define @t447 () (=> @t308 @t446)) % 0.42/0.87 (define @t448 () (=> @t310 @t447)) % 0.42/0.87 (define @t449 () (=> @t312 @t448)) % 0.42/0.87 (define @t450 () (=> @t314 @t449)) % 0.42/0.87 (define @t451 () (=> @t317 @t450)) % 0.42/0.87 (define @t452 () (=> @t319 @t451)) % 0.42/0.87 (define @t453 () (=> @t323 @t452)) % 0.42/0.87 (define @t454 () (=> @t324 @t453)) % 0.42/0.87 (define @t455 () (=> @t335 @t454)) % 0.42/0.87 (define @t456 () (=> @t337 @t455)) % 0.42/0.87 (define @t457 () (=> @t77 @t456)) % 0.42/0.87 (define @t458 () (=> @t344 @t457)) % 0.42/0.87 (define @t459 () (= tptp.id @t70)) % 0.42/0.87 (define @t460 () (=> @t459 @t458)) % 0.42/0.87 (define @t461 () (tptp.comp @t1 tptp.id)) % 0.42/0.87 (define @t462 () (= @t1 @t461)) % 0.42/0.87 (define @t463 () (forall @t46 @t462)) % 0.42/0.87 (define @t464 () (=> @t463 @t460)) % 0.42/0.87 (define @t465 () (=> @t352 @t464)) % 0.42/0.87 (define @t466 () (=> @t357 @t465)) % 0.42/0.87 (define @t467 () (=> @t360 @t466)) % 0.42/0.87 (define @t468 () (tptp.comp tptp.id @t1)) % 0.42/0.87 (define @t469 () (= @t1 @t468)) % 0.42/0.87 (define @t470 () (forall @t46 @t469)) % 0.42/0.87 (define @t471 () (=> @t470 @t467)) % 0.42/0.87 (define @t472 () (=> @t367 @t471)) % 0.42/0.87 (define @t473 () (=> @t374 @t472)) % 0.42/0.87 (define @t474 () (tptp.sub @t5 tptp.id)) % 0.42/0.87 (define @t475 () (= @t5 @t474)) % 0.42/0.87 (define @t476 () (forall @t23 @t475)) % 0.42/0.87 (define @t477 () (=> @t476 @t473)) % 0.42/0.87 (define @t478 () (=> @t379 @t477)) % 0.42/0.87 (define @t479 () (@list @t263)) % 0.42/0.87 (define @t480 () (forall @t479 @t441)) % 0.42/0.87 (define @t481 () (forall @t479 @t264)) % 0.42/0.87 (define @t482 () (@list @t5)) % 0.42/0.87 (define @t483 () (or @t282 @t278 @t440 @t481)) % 0.42/0.87 (define @t484 () (forall @t23 @t275)) % 0.42/0.87 (define @t485 () (or @t282 @t278 @t440 @t484)) % 0.42/0.87 (define @t486 () (or @t278 @t440 @t484)) % 0.42/0.87 (define @t487 () (=> @t439 @t484)) % 0.42/0.87 (define @t488 () (=> @t277 @t487)) % 0.42/0.87 (define @t489 () (or @t437 @t132)) % 0.42/0.87 (define @t490 () (not @t136)) % 0.42/0.87 (define @t491 () (or @t490 @t170)) % 0.42/0.87 (define @t492 () (not @t84)) % 0.42/0.87 (define @t493 () (or @t492 @t490 @t135)) % 0.42/0.87 (define @t494 () (not @t80)) % 0.42/0.87 (define @t495 () (or @t494 @t84)) % 0.42/0.87 (define @t496 () (or @t290 @t287)) % 0.42/0.87 (define @t497 () (or @t278 @t440 @t496)) % 0.42/0.87 (define @t498 () (forall @t291 @t497)) % 0.42/0.87 (define @t499 () (@list @t286 @t285)) % 0.42/0.87 (define @t500 () (forall @t499 @t497)) % 0.42/0.87 (define @t501 () (forall @t499 @t496)) % 0.42/0.87 (define @t502 () (or @t278 @t440 @t501)) % 0.42/0.87 (define @t503 () (_ @t83 @t365)) % 0.42/0.87 (define @t504 () (forall @t19 (or @t299 @t503))) % 0.42/0.87 (define @t505 () (or @t278 @t440 @t504)) % 0.42/0.87 (define @t506 () (=> @t439 @t504)) % 0.42/0.87 (define @t507 () (or @t299 @t165)) % 0.42/0.87 (define @t508 () (not @t153)) % 0.42/0.87 (define @t509 () (or @t508 @t152)) % 0.42/0.87 (define @t510 () (or @t295 @t294)) % 0.42/0.87 (define @t511 () (or @t299 @t276 @t510)) % 0.42/0.87 (define @t512 () (forall @t301 @t511)) % 0.42/0.87 (define @t513 () (@list @t293)) % 0.42/0.87 (define @t514 () (forall @t513 @t511)) % 0.42/0.87 (define @t515 () (forall @t513 @t510)) % 0.42/0.87 (define @t516 () (or @t299 @t276 @t515)) % 0.42/0.87 (define @t517 () (tptp.sub @t2 @t292)) % 0.42/0.87 (define @t518 () (_ @t83 @t517)) % 0.42/0.87 (define @t519 () (forall @t154 (or @t289 @t518))) % 0.42/0.87 (define @t520 () (or @t299 @t492 @t519)) % 0.42/0.87 (define @t521 () (=> @t84 @t519)) % 0.42/0.87 (define @t522 () (or @t508 @t157)) % 0.42/0.87 (define @t523 () (@list @t303)) % 0.42/0.87 (define @t524 () (forall @t523 @t307)) % 0.42/0.87 (define @t525 () (forall @t523 @t304)) % 0.42/0.87 (define @t526 () (or @t282 @t278 @t306 @t525)) % 0.42/0.87 (define @t527 () (or @t282 @t278 @t306 @t484)) % 0.42/0.87 (define @t528 () (or @t278 @t306 @t484)) % 0.42/0.87 (define @t529 () (=> @t305 @t484)) % 0.42/0.87 (define @t530 () (=> @t277 @t529)) % 0.42/0.87 (define @t531 () (or @t492 @t132)) % 0.42/0.87 (define @t532 () (not @t114)) % 0.42/0.87 (define @t533 () (or @t532 @t95)) % 0.42/0.87 (define @t534 () (not @t109)) % 0.42/0.87 (define @t535 () (or @t534 @t95)) % 0.42/0.87 (define @t536 () (not @t101)) % 0.42/0.87 (define @t537 () (or @t536 @t105)) % 0.42/0.87 (define @t538 () (or @t536 @t95)) % 0.42/0.87 (define @t539 () (or @t327 @t326)) % 0.42/0.87 (define @t540 () (or @t332 @t330 @t539)) % 0.42/0.87 (define @t541 () (forall @t334 @t540)) % 0.42/0.87 (define @t542 () (@list @t325)) % 0.42/0.87 (define @t543 () (forall @t542 @t540)) % 0.42/0.87 (define @t544 () (forall @t542 @t539)) % 0.42/0.87 (define @t545 () (or @t332 @t330 @t544)) % 0.42/0.87 (define @t546 () (not @t90)) % 0.42/0.87 (define @t547 () (or @t546 @t330 @t281)) % 0.42/0.87 (define @t548 () (=> @t329 @t281)) % 0.42/0.87 (define @t549 () (or @t494 @t492 @t86)) % 0.42/0.87 (define @t550 () (or @t494 @t79)) % 0.42/0.87 (define @t551 () (= @t1 @t74)) % 0.42/0.87 (define @t552 () (= @t1 @t67)) % 0.42/0.87 (define @t553 () (= @t1 @t50)) % 0.42/0.87 (define @t554 () (= @t1 @t45)) % 0.42/0.87 (define @t555 () (= @t5 @t22)) % 0.42/0.87 (define @t556 () (= @t5 @t18)) % 0.42/0.87 (define @t557 () (@quantifiers_skolemize @t284 0)) % 0.42/0.87 (define @t558 () (_ @t557 @t265)) % 0.42/0.87 (define @t559 () (_ @t557 @t5)) % 0.42/0.87 (define @t560 () (not @t559)) % 0.42/0.87 (define @t561 () (forall @t23 (or @t560 @t558))) % 0.42/0.87 (define @t562 () (@quantifiers_skolemize @t561 0)) % 0.42/0.87 (define @t563 () (not (_ @t557 @t2))) % 0.42/0.87 (define @t564 () (forall @t154 (or @t563 (_ @t557 (tptp.sub @t562 @t268))))) % 0.42/0.87 (define @t565 () (@quantifiers_skolemize @t564 0)) % 0.42/0.87 (define @t566 () (tptp.push @t565 @t267)) % 0.42/0.87 (define @t567 () (forall @t23 (or (not (forall @t154 (or @t563 (_ @t557 @t269)))) @t558))) % 0.42/0.87 (define @t568 () (@quantifiers_skolemize @t284 1)) % 0.42/0.87 (define @t569 () (_ @t557 @t568)) % 0.42/0.87 (define @t570 () (not @t567)) % 0.42/0.87 (define @t571 () (forall @t110 (or @t560 @t563 (_ @t557 @t273)))) % 0.42/0.87 (define @t572 () (not @t571)) % 0.42/0.87 (define @t573 () (forall @t23 (or @t280 @t559))) % 0.42/0.87 (define @t574 () (not @t573)) % 0.42/0.87 (define @t575 () (or @t574 @t572 @t570 @t569)) % 0.42/0.87 (define @t576 () (@list true)) % 0.42/0.87 (define @t577 () (@list @t575)) % 0.42/0.87 (define @t578 () (not @t561)) % 0.42/0.87 (define @t579 () (or @t574 @t572 @t578 @t569)) % 0.42/0.87 (define @t580 () (@list false false true false)) % 0.42/0.87 (define @t581 () (_ @t557 (tptp.lam @t562))) % 0.42/0.87 (define @t582 () (or (not (_ @t557 @t562)) @t581)) % 0.42/0.87 (define @t583 () (not @t564)) % 0.42/0.87 (define @t584 () (or @t583 @t581)) % 0.42/0.87 (define @t585 () (@list true false)) % 0.42/0.87 (define @t586 () (_ @t557 (tptp.sub @t562 @t566))) % 0.42/0.87 (define @t587 () (_ @t557 @t565)) % 0.42/0.87 (define @t588 () (not @t587)) % 0.42/0.87 (define @t589 () (or @t588 @t586)) % 0.42/0.87 (define @t590 () (@list @t589)) % 0.42/0.87 (define @t591 () (forall @t154 (or @t289 (_ @t557 (tptp.sub @t2 @t566))))) % 0.42/0.87 (define @t592 () (not @t591)) % 0.42/0.87 (define @t593 () (or @t572 @t570 @t592 @t586)) % 0.42/0.87 (define @t594 () (@quantifiers_skolemize @t591 0)) % 0.42/0.87 (define @t595 () (_ @t557 (tptp.sub @t594 @t566))) % 0.42/0.87 (define @t596 () (tptp.var @t594)) % 0.42/0.87 (define @t597 () (not @t596)) % 0.42/0.87 (define @t598 () (or @t597 @t595)) % 0.42/0.87 (define @t599 () (@list @t598)) % 0.42/0.87 (define @t600 () (forall @t154 (or @t289 (_ @t557 (tptp.sub @t2 @t267))))) % 0.42/0.87 (define @t601 () (@quantifiers_skolemize @t600 0)) % 0.42/0.87 (define @t602 () (tptp.var @t601)) % 0.42/0.87 (define @t603 () (tptp.sub @t601 @t267)) % 0.42/0.87 (define @t604 () (_ @t557 @t603)) % 0.42/0.87 (define @t605 () (not @t602)) % 0.42/0.87 (define @t606 () (or @t605 @t604)) % 0.42/0.87 (define @t607 () (@list @t601)) % 0.42/0.87 (define @t608 () (_ @t557 @t601)) % 0.42/0.87 (define @t609 () (or @t605 @t608)) % 0.42/0.87 (define @t610 () (not @t608)) % 0.42/0.87 (define @t611 () (= @t601 @t603)) % 0.42/0.87 (define @t612 () (not @t611)) % 0.42/0.87 (define @t613 () (not @t604)) % 0.42/0.87 (define @t614 () (and @t613 @t611)) % 0.42/0.87 (define @t615 () (not @t606)) % 0.42/0.87 (define @t616 () (not @t600)) % 0.42/0.87 (define @t617 () (or @t616 @t588 @t597 @t595)) % 0.42/0.87 (define @t618 () (not @t617)) % 0.42/0.87 (assume @p1 @t15) % 0.42/0.87 (assume @p2 @t21) % 0.42/0.87 (assume @p3 @t25) % 0.42/0.87 (assume @p4 @t36) % 0.42/0.87 (assume @p5 @t44) % 0.42/0.87 (assume @p6 @t48) % 0.42/0.87 (assume @p7 @t52) % 0.42/0.87 (assume @p8 @t60) % 0.42/0.87 (assume @p9 @t66) % 0.42/0.87 (assume @p10 @t69) % 0.42/0.87 (assume @p11 @t71) % 0.42/0.87 (assume @p12 @t76) % 0.42/0.87 (assume @p13 (= tptp.ulamvar1 @t77)) % 0.42/0.87 (assume @p14 @t82) % 0.42/0.87 (assume @p15 @t94) % 0.42/0.87 (assume @p16 @t104) % 0.42/0.87 (assume @p17 @t107) % 0.42/0.87 (assume @p18 @t112) % 0.42/0.87 (assume @p19 @t116) % 0.42/0.87 (assume @p20 @t122) % 0.42/0.87 (assume @p21 @t126) % 0.42/0.87 (assume @p22 @t130) % 0.42/0.87 (assume @p23 @t142) % 0.42/0.87 (assume @p24 (= tptp.pushprop_lem0 (forall @t146 (exists @t145 @t144)))) % 0.42/0.87 (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))))))))))))))))))))))))) % 0.42/0.87 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.42/0.87 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t83 @t148 @t5 @t1 @t2) (=> @t84 (_ @t148 (_ @t6 (_ @t147 @t1))))))) % 0.42/0.87 (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))))))))))))))))))))))))) % 0.42/0.87 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.42/0.87 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t149 (=> @t84 (=> @t144 (_ @t143 tptp.one)))))) % 0.42/0.87 (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))))))))))))))))))))))))) % 0.42/0.87 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.42/0.87 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t149 (=> @t144 (=> @t155 (forall @t151 (=> (_ tptp.var @t99) (=> (_ @t143 @t99) (_ @t143 (_ @t150 tptp.sh)))))))))) % 0.42/0.87 (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))))))))))))))))))))))))) % 0.42/0.87 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.42/0.87 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t149 (=> @t144 (=> (forall @t154 (=> @t153 @t159)) @t158))))) % 0.42/0.87 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.42/0.87 (assume @p38 @t163) % 0.42/0.87 (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))))))))))))))))))))))))) % 0.42/0.87 (assume @p40 (= tptp.pushprop_lthm_orig @t164)) % 0.42/0.87 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t164))) % 0.42/0.87 (assume @p42 @t177) % 0.42/0.87 (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 @t178)))))))))))))))))))))))) % 0.42/0.87 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t178)))))))))) % 0.42/0.87 (assume @p45 @t183) % 0.42/0.87 (assume @p46 @t209) % 0.42/0.87 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t184))) % 0.42/0.87 (assume @p48 (= tptp.substmonoid (and @t59 @t47 @t68))) % 0.42/0.87 (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)))))))))))))))))))))))))))) % 0.42/0.87 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.42/0.87 (assume @p51 (= tptp.termmset (and @t43 @t24))) % 0.42/0.87 (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))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.42/0.87 (assume @p54 (= tptp.hoasapinj1 (forall @t102 (=> @t212 @t95)))) % 0.42/0.87 (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)))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.42/0.87 (assume @p57 (= tptp.hoasapinj2 (forall @t102 (=> @t212 @t105)))) % 0.42/0.87 (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))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.42/0.87 (assume @p60 (= tptp.hoaslaminj (forall @t225 (=> @t224 (forall (@list @t213) (=> (forall @t221 (= (_ (_ tptp.sub @t214) @t37) (_ (_ @t213 @t38) @t61))) (=> (= @t220 (_ @t219 (lambda @t218 @t214))) (forall @t218 (= @t217 @t214))))))))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.42/0.87 (assume @p63 (= tptp.hoaslamnotap (forall @t225 (=> @t224 (forall @t110 (not (= (_ @t219 (lambda (@list @t1 @t99) (_ @t216 @t99))) @t226))))))) % 0.42/0.87 (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))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.42/0.87 (assume @p66 (= tptp.hoaslamnotvar (forall @t225 (=> @t224 (not (_ (_ @t227 @t220) tptp.id)))))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.42/0.87 (assume @p69 (= tptp.hoasapnotvar (forall @t110 (not (_ (_ @t227 @t226) tptp.id))))) % 0.42/0.87 (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))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.42/0.87 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t230 (exists @t145 @t229)))) % 0.42/0.87 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.42/0.87 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t240 (=> @t239 (=> @t238 (=> @t234 (=> @t229 (forall @t23 (=> @t80 @t231))))))))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t240 (=> @t239 (=> @t238 (=> @t242 (=> @t229 (forall @t110 (=> @t231 (=> @t159 (_ @t143 @t10))))))))))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t154 (exists @t225 (forall @t19 (= @t217 @t156)))))) % 0.42/0.87 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.42/0.87 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t240 (=> @t239 (=> @t238 @t245))))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.42/0.87 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t240 @t245))) % 0.42/0.87 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.42/0.87 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t230 (=> @t239 (=> @t238 (=> @t234 (forall @t23 (=> @t80 @t233)))))))) % 0.42/0.87 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t246)) % 0.42/0.87 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t246)) % 0.42/0.87 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t230 (=> @t239 (=> @t238 (=> @t242 (forall @t110 (=> @t233 (=> @t241 (_ (_ @t232 @t10) tptp.id)))))))))) % 0.42/0.87 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t247)) % 0.42/0.87 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t247)) % 0.42/0.87 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t230 (=> @t244 @t249)))) % 0.42/0.87 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.42/0.87 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t230 (=> (forall @t225 (=> (exists @t151 (forall @t221 (and (= @t223 (_ (_ tptp.sub (_ @t150 @t16)) @t37)) (= (_ @t150 @t62) @t222)))) @t243)) @t249)))) % 0.42/0.87 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t230 (=> @t239 (=> @t238 @t250))))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.42/0.87 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t230 @t250))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.42/0.87 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t154 (exists @t225 (= (_ @t3 @t70) @t251))))) % 0.42/0.87 (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)))))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.42/0.87 (assume @p103 (= tptp.hoasinduction (forall @t230 (=> @t239 (=> @t238 (=> @t234 @t252)))))) % 0.42/0.87 (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 @t253)))))))))))))))))))))))))))))))))))) % 0.42/0.87 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t253))) % 0.42/0.87 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.42/0.87 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t230 @t252))) % 0.42/0.87 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.42/0.87 (assume @p109 @t254) % 0.42/0.87 (assume @p110 true) % 0.42/0.87 (step @p111 (= tptp.pushprop_p_and_p_prime @t258) :rule refl :args (@t258)) % 0.42/0.87 (step @p112 (= tptp.hoasap @t259) :rule refl :args (@t259)) % 0.42/0.87 (step @p113 (= tptp.hoaslam @t260) :rule refl :args (@t260)) % 0.42/0.87 (step @p114 (= tptp.hoasvar @t261) :rule refl :args (@t261)) % 0.42/0.87 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t262) :rule refl :args (@t262)) % 0.42/0.87 (step @p116 :rule refl :args (@t338)) % 0.42/0.87 (step @p117 :rule refl :args (@t339)) % 0.42/0.87 (step @p118 :rule refl :args (@t77)) % 0.42/0.87 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t77 @t339))) % 0.42/0.87 (step @p120 :rule symm :premises (@p119)) % 0.42/0.87 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 0.42/0.87 (step @p122 :rule cong :premises (@p121 @p116) :args (@t340)) % 0.42/0.87 (step @p123 :rule refl :args (@t344)) % 0.42/0.87 (step @p124 :rule cong :premises (@p123 @p122) :args (@t345)) % 0.42/0.87 (step @p125 :rule refl :args (@t346)) % 0.42/0.87 (step @p126 :rule cong :premises (@p125 @p124) :args (@t347)) % 0.42/0.87 (step @p127 :rule refl :args (@t352)) % 0.42/0.87 (step @p128 :rule cong :premises (@p127 @p126) :args (@t353)) % 0.42/0.87 (step @p129 :rule refl :args (@t357)) % 0.42/0.87 (step @p130 :rule cong :premises (@p129 @p128) :args (@t358)) % 0.42/0.87 (step @p131 :rule refl :args (@t360)) % 0.42/0.87 (step @p132 :rule cong :premises (@p131 @p130) :args (@t361)) % 0.42/0.87 (step @p133 :rule refl :args (@t362)) % 0.42/0.87 (step @p134 :rule cong :premises (@p133 @p132) :args (@t363)) % 0.42/0.87 (step @p135 :rule refl :args (@t367)) % 0.42/0.87 (step @p136 :rule cong :premises (@p135 @p134) :args (@t368)) % 0.42/0.87 (step @p137 :rule refl :args (@t374)) % 0.42/0.87 (step @p138 :rule cong :premises (@p137 @p136) :args (@t375)) % 0.42/0.87 (step @p139 :rule refl :args (@t376)) % 0.42/0.87 (step @p140 :rule cong :premises (@p139 @p138) :args (@t377)) % 0.42/0.87 (step @p141 :rule refl :args (@t379)) % 0.42/0.87 (step @p142 :rule cong :premises (@p141 @p140) :args (@t380)) % 0.42/0.87 (step @p143 :rule refl :args (@t383)) % 0.42/0.87 (step @p144 :rule cong :premises (@p143 @p142) :args (@t384)) % 0.42/0.87 (step @p145 :rule cong :premises (@p144) :args ((not @t384))) % 0.42/0.87 (step @p146 :rule bool-impl-true2 :args (@t345)) % 0.42/0.87 (step @p147 :rule refl :args (@t264)) % 0.42/0.87 (step @p148 :rule refl :args (@t266)) % 0.42/0.87 (step @p149 :rule refl :args (@t267)) % 0.42/0.87 (step @p150 :rule refl :args (@t70)) % 0.42/0.87 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t70 @t267))) % 0.42/0.87 (step @p152 :rule symm :premises (@p151)) % 0.42/0.87 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.42/0.87 (step @p154 :rule refl :args (@t2)) % 0.42/0.87 (step @p155 :rule cong :premises (@p154 @p153) :args (@t385)) % 0.42/0.87 (step @p156 :rule refl :args (@t5)) % 0.42/0.87 (step @p157 :rule cong :premises (@p156 @p155) :args (@t386)) % 0.42/0.87 (step @p158 :rule cong :premises (@p157) :args (@t387)) % 0.42/0.87 (step @p159 :rule refl :args (@t271)) % 0.42/0.87 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t388)) % 0.42/0.87 (step @p161 :rule cong :premises (@p160) :args (@t389)) % 0.42/0.87 (step @p162 :rule cong :premises (@p161) :args (@t390)) % 0.42/0.87 (step @p163 :rule nary_cong :premises (@p162 @p148) :args (@t391)) % 0.42/0.87 (step @p164 :rule cong :premises (@p163) :args (@t392)) % 0.42/0.87 (step @p165 :rule cong :premises (@p164) :args (@t393)) % 0.42/0.87 (step @p166 :rule refl :args (@t278)) % 0.42/0.87 (step @p167 :rule refl :args (@t282)) % 0.42/0.87 (step @p168 :rule nary_cong :premises (@p167 @p166 @p165 @p147) :args (@t394)) % 0.42/0.87 (step @p169 :rule cong :premises (@p168) :args (@t395)) % 0.42/0.87 (step @p170 :rule refl :args (@t287)) % 0.42/0.87 (step @p171 :rule refl :args (@t290)) % 0.42/0.87 (step @p172 :rule nary_cong :premises (@p166 @p165 @p171 @p170) :args (@t396)) % 0.42/0.87 (step @p173 :rule cong :premises (@p172) :args (@t397)) % 0.42/0.87 (step @p174 :rule cong :premises (@p173 @p169) :args (@t398)) % 0.42/0.87 (step @p175 :rule refl :args (@t302)) % 0.42/0.87 (step @p176 :rule cong :premises (@p175 @p174) :args (@t399)) % 0.42/0.87 (step @p177 :rule refl :args (@t308)) % 0.42/0.87 (step @p178 :rule cong :premises (@p177 @p176) :args (@t400)) % 0.42/0.87 (step @p179 :rule refl :args (@t310)) % 0.42/0.87 (step @p180 :rule cong :premises (@p179 @p178) :args (@t401)) % 0.42/0.87 (step @p181 :rule refl :args (@t312)) % 0.42/0.87 (step @p182 :rule cong :premises (@p181 @p180) :args (@t402)) % 0.42/0.87 (step @p183 :rule refl :args (@t314)) % 0.42/0.87 (step @p184 :rule cong :premises (@p183 @p182) :args (@t403)) % 0.42/0.87 (step @p185 :rule refl :args (@t317)) % 0.42/0.87 (step @p186 :rule cong :premises (@p185 @p184) :args (@t404)) % 0.42/0.87 (step @p187 :rule refl :args (@t319)) % 0.42/0.87 (step @p188 :rule cong :premises (@p187 @p186) :args (@t405)) % 0.42/0.87 (step @p189 :rule refl :args (@t323)) % 0.42/0.87 (step @p190 :rule cong :premises (@p189 @p188) :args (@t406)) % 0.42/0.87 (step @p191 :rule refl :args (@t324)) % 0.42/0.87 (step @p192 :rule cong :premises (@p191 @p190) :args (@t407)) % 0.42/0.87 (step @p193 :rule refl :args (@t335)) % 0.42/0.87 (step @p194 :rule cong :premises (@p193 @p192) :args (@t408)) % 0.42/0.87 (step @p195 :rule refl :args (@t337)) % 0.42/0.87 (step @p196 :rule cong :premises (@p195 @p194) :args (@t409)) % 0.42/0.87 (step @p197 :rule refl :args (@t77)) % 0.42/0.87 (step @p198 :rule cong :premises (@p197 @p196) :args (@t410)) % 0.42/0.87 (step @p199 :rule cong :premises (@p123 @p198) :args (@t411)) % 0.42/0.87 (step @p200 :rule eq-refl :args (@t70)) % 0.42/0.87 (step @p201 :rule cong :premises (@p200 @p199) :args (@t412)) % 0.42/0.87 (step @p202 :rule trans :premises (@p201 @p146)) % 0.42/0.87 (step @p203 :rule refl :args (@t1)) % 0.42/0.87 (step @p204 :rule cong :premises (@p203 @p153) :args (@t413)) % 0.42/0.87 (step @p205 :rule cong :premises (@p203 @p204) :args (@t414)) % 0.42/0.87 (step @p206 :rule cong :premises (@p205) :args (@t415)) % 0.42/0.87 (step @p207 :rule cong :premises (@p206 @p202) :args (@t416)) % 0.42/0.87 (step @p208 :rule cong :premises (@p127 @p207) :args (@t417)) % 0.42/0.87 (step @p209 :rule cong :premises (@p129 @p208) :args (@t418)) % 0.42/0.87 (step @p210 :rule cong :premises (@p131 @p209) :args (@t419)) % 0.42/0.87 (step @p211 :rule cong :premises (@p153 @p203) :args (@t420)) % 0.42/0.87 (step @p212 :rule cong :premises (@p203 @p211) :args (@t421)) % 0.42/0.87 (step @p213 :rule cong :premises (@p212) :args (@t422)) % 0.42/0.87 (step @p214 :rule cong :premises (@p213 @p210) :args (@t423)) % 0.42/0.87 (step @p215 :rule cong :premises (@p135 @p214) :args (@t424)) % 0.42/0.87 (step @p216 :rule cong :premises (@p137 @p215) :args (@t425)) % 0.42/0.87 (step @p217 :rule cong :premises (@p156 @p153) :args (@t426)) % 0.42/0.87 (step @p218 :rule cong :premises (@p156 @p217) :args (@t427)) % 0.42/0.87 (step @p219 :rule cong :premises (@p218) :args (@t428)) % 0.42/0.87 (step @p220 :rule cong :premises (@p219 @p216) :args (@t429)) % 0.42/0.87 (step @p221 :rule cong :premises (@p141 @p220) :args (@t430)) % 0.42/0.87 (step @p222 :rule cong :premises (@p143 @p221) :args (@t431)) % 0.42/0.87 (step @p223 :rule cong :premises (@p222) :args ((not @t431))) % 0.42/0.87 (step @p224 :rule eq-symm :args (@t70 tptp.id)) % 0.42/0.87 (step @p225 :rule refl :args (tptp.axvarshift)) % 0.42/0.87 (step @p226 :rule cong :premises (@p225 @p224) :args (@t71)) % 0.42/0.87 (step @p227 :rule eq_resolve :premises (@p11 @p226)) % 0.42/0.87 (step @p228 :rule equiv_elim2 :premises (@p46)) % 0.42/0.87 (step @p229 :rule resolution :premises (@p228 @p109) :args (true tptp.induction2_gthm)) % 0.42/0.87 (step @p230 :rule not_implies_elim2 :premises (@p229)) % 0.42/0.87 (step @p231 :rule not_implies_elim2 :premises (@p230)) % 0.42/0.87 (step @p232 :rule not_implies_elim2 :premises (@p231)) % 0.42/0.87 (step @p233 :rule not_implies_elim2 :premises (@p232)) % 0.42/0.87 (step @p234 :rule not_implies_elim2 :premises (@p233)) % 0.42/0.87 (step @p235 :rule not_implies_elim2 :premises (@p234)) % 0.42/0.87 (step @p236 :rule not_implies_elim2 :premises (@p235)) % 0.42/0.87 (step @p237 :rule not_implies_elim2 :premises (@p236)) % 0.42/0.87 (step @p238 :rule not_implies_elim2 :premises (@p237)) % 0.42/0.87 (step @p239 :rule not_implies_elim2 :premises (@p238)) % 0.42/0.87 (step @p240 :rule not_implies_elim1 :premises (@p239)) % 0.42/0.87 (step @p241 :rule eq_resolve :premises (@p240 @p227)) % 0.42/0.87 (step @p242 :rule refl :args (@t2)) % 0.42/0.87 (step @p243 :rule cong :premises (@p242 @p241) :args (@t432)) % 0.42/0.87 (step @p244 :rule refl :args (@t5)) % 0.42/0.87 (step @p245 :rule cong :premises (@p244 @p243) :args (@t433)) % 0.42/0.87 (step @p246 :rule cong :premises (@p245) :args (@t434)) % 0.42/0.87 (step @p247 :rule refl :args (@t271)) % 0.42/0.87 (step @p248 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:premises (@p1154 @p1171) :args ((or @t575 (not @t574)))) % 0.42/0.88 (step @p1173 :rule cnf_or_neg :args (@t575 0)) % 0.42/0.88 (step @p1174 :rule eq_resolve :premises (@p1173 @p1172)) % 0.42/0.88 (step @p1175 :rule reordering :premises (@p1174) :args ((or @t573 @t575))) % 0.42/0.88 (step @p1176 :rule chain_m_resolution :premises (@p1175 @p1152) :args (@t573 @t576 @t577)) % 0.42/0.88 (step @p1177 :rule cnf_or_pos :args (@t579)) % 0.42/0.88 (step @p1178 :rule reordering :premises (@p1177) :args ((or @t574 @t572 @t569 @t578 (not @t579)))) % 0.42/0.88 (step @p1179 :rule chain_m_resolution :premises (@p1178 @p1176 @p1170 @p1164 @p1162) :args (@t578 @t580 (@list @t573 @t571 @t569 @t579))) % 0.42/0.88 (step @p1180 :rule skolemize :premises (@p1179)) % 0.42/0.88 (step @p1181 :rule cnf_or_neg :args (@t582 1)) % 0.42/0.88 (step @p1182 :rule chain_m_resolution :premises (@p1181 @p1180) :args ((not @t581) @t576 (@list @t582))) % 0.42/0.88 (step @p1183 :rule cnf_or_pos :args (@t584)) % 0.42/0.88 (step @p1184 :rule reordering :premises (@p1183) :args ((or @t581 @t583 (not @t584)))) % 0.42/0.88 (step @p1185 :rule chain_m_resolution :premises (@p1184 @p1182 @p1160) :args (@t583 @t585 (@list @t581 @t584))) % 0.42/0.88 (step @p1186 :rule skolemize :premises (@p1185)) % 0.42/0.88 (step @p1187 :rule cnf_or_neg :args (@t589 1)) % 0.42/0.88 (step @p1188 :rule chain_m_resolution :premises (@p1187 @p1186) :args ((not @t586) @t576 @t590)) % 0.42/0.88 (step @p1189 :rule cnf_or_pos :args (@t593)) % 0.42/0.88 (step @p1190 :rule reordering :premises (@p1189) :args ((or @t572 @t570 @t586 @t592 (not @t593)))) % 0.42/0.88 (step @p1191 :rule chain_m_resolution :premises (@p1190 @p1170 @p1159 @p1188 @p1150) :args (@t592 @t580 (@list @t571 @t567 @t586 @t593))) % 0.42/0.88 (step @p1192 :rule skolemize :premises (@p1191)) % 0.42/0.88 (step @p1193 :rule cnf_or_neg :args (@t598 1)) % 0.42/0.88 (step @p1194 :rule chain_m_resolution :premises (@p1193 @p1192) :args ((not @t595) @t576 @t599)) % 0.42/0.88 (step @p1195 :rule bool-double-not-elim :args (@t596)) % 0.42/0.88 (step @p1196 :rule refl :args (@t598)) % 0.42/0.88 (step @p1197 :rule nary_cong :premises (@p1196 @p1195) :args ((or @t598 (not @t597)))) % 0.42/0.88 (step @p1198 :rule cnf_or_neg :args (@t598 0)) % 0.42/0.88 (step @p1199 :rule eq_resolve :premises (@p1198 @p1197)) % 0.42/0.88 (step @p1200 :rule reordering :premises (@p1199) :args ((or @t596 @t598))) % 0.42/0.88 (step @p1201 :rule chain_m_resolution :premises (@p1200 @p1192) :args (@t596 @t576 @t599)) % 0.42/0.88 (step @p1202 :rule bool-double-not-elim :args (@t602)) % 0.42/0.88 (step @p1203 :rule refl :args (@t606)) % 0.42/0.88 (step @p1204 :rule nary_cong :premises (@p1203 @p1202) :args ((or @t606 (not @t605)))) % 0.42/0.88 (step @p1205 :rule cnf_or_neg :args (@t606 0)) % 0.42/0.88 (step @p1206 :rule eq_resolve :premises (@p1205 @p1204)) % 0.42/0.88 (step @p1207 :rule reordering :premises (@p1206) :args ((or @t602 @t606))) % 0.42/0.88 (step @p1208 :rule cnf_or_neg :args (@t606 1)) % 0.42/0.88 (step @p1209 :rule instantiate :premises (@p1176) :args (@t607)) % 0.42/0.88 (step @p1210 :rule cnf_or_pos :args (@t609)) % 0.42/0.88 (step @p1211 :rule reordering :premises (@p1210) :args ((or @t605 @t608 (not @t609)))) % 0.42/0.88 (step @p1212 :rule not_implies_elim1 :premises (@p1126)) % 0.42/0.88 (step @p1213 :rule instantiate :premises (@p1212) :args (@t607)) % 0.42/0.88 (step @p1214 :rule refl :args (@t610)) % 0.42/0.88 (step @p1215 :rule refl :args (@t612)) % 0.42/0.88 (step @p1216 :rule bool-double-not-elim :args (@t604)) % 0.42/0.88 (step @p1217 :rule nary_cong :premises (@p1216 @p1215 @p1214) :args ((or (not @t613) @t612 @t610))) % 0.42/0.88 (assume-push @p1265 @t613) % 0.42/0.88 (assume-push @p1266 @t611) % 0.42/0.88 (assume-push @p1267 @t613) % 0.42/0.88 (assume-push @p1268 @t611) % 0.42/0.88 (step @p1222 :rule false_intro :premises (@p1265)) % 0.42/0.88 (step @p1223 :rule cong :premises (@p1213) :args (@t608)) % 0.42/0.88 (step @p1224 :rule trans :premises (@p1223 @p1222)) % 0.42/0.88 (step @p1225 :rule false_elim :premises (@p1224)) % 0.42/0.88 (step-pop @p1269 :rule scope :premises (@p1225)) % 0.42/0.88 (step-pop @p1270 :rule scope :premises (@p1269)) % 0.42/0.88 (step @p1226 :rule process_scope :premises (@p1270) :args (@t610)) % 0.42/0.88 (step @p1229 :rule and_intro :premises (@p1265 @p1213)) % 0.42/0.88 (step @p1230 :rule modus_ponens :premises (@p1229 @p1226)) % 0.42/0.88 (step-pop @p1271 :rule scope :premises (@p1230)) % 0.42/0.88 (step-pop @p1272 :rule scope :premises (@p1271)) % 0.42/0.88 (step @p1231 :rule process_scope :premises (@p1272) :args (@t610)) % 0.42/0.88 (step @p1234 :rule implies_elim :premises (@p1231)) % 0.42/0.88 (step @p1235 :rule cnf_and_neg :args (@t614)) % 0.42/0.88 (step @p1236 :rule resolution :premises (@p1235 @p1234) :args (true @t614)) % 0.42/0.88 (step @p1237 :rule eq_resolve :premises (@p1236 @p1217)) % 0.42/0.88 (step @p1238 :rule chain_m_resolution :premises (@p1237 @p1213 @p1211 @p1209 @p1208 @p1207) :args (@t606 (@list false false false true false) (@list @t611 @t608 @t609 @t604 @t602))) % 0.42/0.88 (step @p1239 :rule refl :args (@t615)) % 0.42/0.88 (step @p1240 :rule bool-double-not-elim :args (@t600)) % 0.42/0.88 (step @p1241 :rule nary_cong :premises (@p1240 @p1239) :args ((or (not @t616) @t615))) % 0.42/0.88 (assume-push @p1273 @t616) % 0.42/0.88 (step @p1243 :rule skolemize :premises (@p1273)) % 0.42/0.88 (step-pop @p1274 :rule scope :premises (@p1243)) % 0.42/0.88 (step @p1244 :rule process_scope :premises (@p1274) :args (@t615)) % 0.42/0.88 (step @p1246 :rule implies_elim :premises (@p1244)) % 0.42/0.88 (step @p1247 :rule eq_resolve :premises (@p1246 @p1241)) % 0.42/0.88 (step @p1248 :rule chain_m_resolution :premises (@p1247 @p1238) :args (@t600 (@list false) (@list @t606))) % 0.42/0.88 (step @p1249 :rule bool-double-not-elim :args (@t587)) % 0.42/0.88 (step @p1250 :rule refl :args (@t589)) % 0.42/0.88 (step @p1251 :rule nary_cong :premises (@p1250 @p1249) :args ((or @t589 (not @t588)))) % 0.42/0.88 (step @p1252 :rule cnf_or_neg :args (@t589 0)) % 0.42/0.88 (step @p1253 :rule eq_resolve :premises (@p1252 @p1251)) % 0.42/0.88 (step @p1254 :rule reordering :premises (@p1253) :args ((or @t587 @t589))) % 0.42/0.88 (step @p1255 :rule chain_m_resolution :premises (@p1254 @p1186) :args (@t587 @t576 @t590)) % 0.42/0.88 (step @p1256 :rule cnf_or_pos :args (@t617)) % 0.42/0.88 (step @p1257 :rule reordering :premises (@p1256) :args ((or @t588 @t616 @t597 @t595 @t618))) % 0.42/0.88 (step @p1258 :rule chain_m_resolution :premises (@p1257 @p1255 @p1248 @p1201 @p1194) :args (@t618 (@list false false false true) (@list @t587 @t600 @t596 @t595))) % 0.42/0.88 (assume-push @p1275 @t302) % 0.42/0.88 (step @p1260 :rule instantiate :premises (@p1147) :args ((@list @t557 @t565 @t267 @t594))) % 0.42/0.88 (step-pop @p1276 :rule scope :premises (@p1260)) % 0.42/0.88 (step @p1261 :rule process_scope :premises (@p1276) :args (@t617)) % 0.42/0.88 (step @p1263 :rule implies_elim :premises (@p1261)) % 0.42/0.88 (step @p1264 false :rule chain_m_resolution :premises (@p1263 @p1258 @p1147) :args (false @t585 (@list @t617 @t302))) % 0.42/0.88 ) % 0.42/0.88 % SZS output end Proof % 0.42/0.88 % cvc5 exiting %------------------------------------------------------------------------------