%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG257^2 : 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 08:05:40 AM UTC 2026 % Result : Theorem 0.42s 0.72s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG257^2 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n018.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Wed Jun 3 01:55:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.40/0.57 %----Proving TH0 % 0.42/0.72 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.42/0.72 % SZS status Theorem % 0.42/0.72 % SZS output start Proof % 0.42/0.72 ( % 0.42/0.72 (declare-sort tptp.term 0) % 0.42/0.72 (declare-sort tptp.subst 0) % 0.42/0.72 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.42/0.72 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.42/0.72 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.42/0.72 (declare-const tptp.one tptp.term) % 0.42/0.72 (declare-const tptp.sh tptp.subst) % 0.42/0.72 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.42/0.72 (declare-const tptp.var (-> tptp.term Bool)) % 0.42/0.72 (declare-const tptp.id tptp.subst) % 0.42/0.72 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3b Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3a Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3 Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem2 Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem1 Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasinduction_lem0 Bool) % 0.42/0.72 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasapnotvar Bool) % 0.42/0.72 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.42/0.72 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.42/0.72 (declare-const tptp.hoaslamnotvar Bool) % 0.42/0.72 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.42/0.72 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.42/0.72 (declare-const tptp.hoaslamnotap Bool) % 0.42/0.72 (declare-const tptp.hoaslaminj_lthm Bool) % 0.42/0.72 (declare-const tptp.hoaslaminj_gthm Bool) % 0.42/0.72 (declare-const tptp.hoaslaminj Bool) % 0.42/0.72 (declare-const tptp.hoasapinj2_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasapinj2_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasapinj2 Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.42/0.72 (declare-const tptp.axassoc Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.42/0.72 (declare-const tptp.axvarcons Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem0 Bool) % 0.42/0.72 (declare-const tptp.apinj1 Bool) % 0.42/0.72 (declare-const tptp.induction Bool) % 0.42/0.72 (declare-const tptp.apnotvar Bool) % 0.42/0.72 (declare-const tptp.laminj Bool) % 0.42/0.72 (declare-const tptp.axvarshift Bool) % 0.42/0.72 (declare-const tptp.ulamvarind Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.42/0.72 (declare-const tptp.ulamvarsh Bool) % 0.42/0.72 (declare-const tptp.ulamvar1 Bool) % 0.42/0.72 (declare-const tptp.axabs Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem1 Bool) % 0.42/0.72 (declare-const tptp.shinj Bool) % 0.42/0.72 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.42/0.72 (declare-const tptp.apinj2 Bool) % 0.42/0.72 (declare-const tptp.axvarid Bool) % 0.42/0.72 (declare-const tptp.axidl Bool) % 0.42/0.72 (declare-const tptp.axclos Bool) % 0.42/0.72 (declare-const tptp.termmset Bool) % 0.42/0.72 (declare-const tptp.axshiftcons Bool) % 0.42/0.72 (declare-const tptp.lamnotap Bool) % 0.42/0.72 (declare-const tptp.lamnotvar Bool) % 0.42/0.72 (declare-const tptp.axapp Bool) % 0.42/0.72 (declare-const tptp.axscons Bool) % 0.42/0.72 (declare-const tptp.axmap Bool) % 0.42/0.72 (declare-const tptp.axidr Bool) % 0.42/0.72 (declare-const tptp.induction2lem Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasapinj1_lthm Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem1v2 Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.42/0.72 (declare-const tptp.induction2 Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem2v2 Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem3v2 Bool) % 0.42/0.72 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.42/0.72 (declare-const tptp.pushprop Bool) % 0.42/0.72 (declare-const tptp.pushprop_gthm Bool) % 0.42/0.72 (declare-const tptp.hoasapinj1 Bool) % 0.42/0.72 (declare-const tptp.pushprop_lthm_orig Bool) % 0.42/0.72 (declare-const tptp.pushprop_lthm Bool) % 0.42/0.72 (declare-const tptp.induction2lem_gthm Bool) % 0.42/0.72 (declare-const tptp.induction2lem_lthm Bool) % 0.42/0.72 (declare-const tptp.induction2_gthm Bool) % 0.42/0.72 (declare-const tptp.induction2_lthm Bool) % 0.42/0.72 (declare-const tptp.substmonoid Bool) % 0.42/0.72 (declare-const tptp.substmonoid_gthm Bool) % 0.42/0.72 (declare-const tptp.termmset_gthm Bool) % 0.42/0.72 (declare-const tptp.substmonoid_lthm Bool) % 0.42/0.72 (declare-const tptp.termmset_lthm Bool) % 0.42/0.72 (declare-const tptp.hoasapinj1_gthm Bool) % 0.42/0.72 (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)))))))))))) % 0.42/0.72 (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)))))) % 0.42/0.72 (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))))) % 0.42/0.72 (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)))))) % 0.42/0.72 (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)))))))) % 0.42/0.72 (define @t1 () (@var "M" tptp.subst)) % 0.42/0.72 (define @t2 () (@var "B" tptp.term)) % 0.42/0.72 (define @t3 () (_ tptp.sub @t2)) % 0.42/0.72 (define @t4 () (_ @t3 @t1)) % 0.42/0.72 (define @t5 () (@var "A" tptp.term)) % 0.42/0.72 (define @t6 () (_ tptp.sub @t5)) % 0.42/0.72 (define @t7 () (_ @t6 @t1)) % 0.42/0.72 (define @t8 () (_ tptp.ap @t5)) % 0.42/0.72 (define @t9 () (_ @t8 @t2)) % 0.42/0.72 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.42/0.72 (define @t11 () (_ tptp.sub tptp.one)) % 0.42/0.72 (define @t12 () (@list @t5 @t1)) % 0.42/0.72 (define @t13 () (_ @t6 tptp.id)) % 0.42/0.72 (define @t14 () (@list @t5)) % 0.42/0.72 (define @t15 () (forall @t14 (= @t13 @t5))) % 0.42/0.72 (define @t16 () (_ tptp.comp @t1)) % 0.42/0.72 (define @t17 () (_ tptp.push tptp.one)) % 0.42/0.72 (define @t18 () (_ tptp.lam @t5)) % 0.42/0.72 (define @t19 () (@var "N" tptp.subst)) % 0.42/0.72 (define @t20 () (_ @t16 @t19)) % 0.42/0.72 (define @t21 () (@list @t5 @t1 @t19)) % 0.42/0.72 (define @t22 () (forall @t21 (= (_ (_ tptp.sub @t7) @t19) (_ @t6 @t20)))) % 0.42/0.72 (define @t23 () (@list @t1)) % 0.42/0.72 (define @t24 () (forall @t23 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 0.42/0.72 (define @t25 () (_ tptp.comp tptp.sh)) % 0.42/0.72 (define @t26 () (@var "K" tptp.subst)) % 0.42/0.72 (define @t27 () (forall (@list @t1 @t19 @t26) (= (_ (_ tptp.comp @t20) @t26) (_ @t16 (_ (_ tptp.comp @t19) @t26))))) % 0.42/0.72 (define @t28 () (_ @t6 @t19)) % 0.42/0.72 (define @t29 () (_ (_ tptp.push @t28) @t20)) % 0.42/0.72 (define @t30 () (forall @t23 (= (_ @t16 tptp.id) @t1))) % 0.42/0.72 (define @t31 () (_ @t17 tptp.sh)) % 0.42/0.72 (define @t32 () (_ @t6 tptp.sh)) % 0.42/0.72 (define @t33 () (_ tptp.var @t5)) % 0.42/0.72 (define @t34 () (@var "P" (-> tptp.term Bool))) % 0.42/0.72 (define @t35 () (_ @t34 @t5)) % 0.42/0.72 (define @t36 () (forall @t14 (=> @t33 @t35))) % 0.42/0.72 (define @t37 () (@list @t34)) % 0.42/0.72 (define @t38 () (= @t5 @t2)) % 0.42/0.72 (define @t39 () (@var "D" tptp.term)) % 0.42/0.72 (define @t40 () (_ tptp.ap @t2)) % 0.42/0.72 (define @t41 () (_ @t40 @t39)) % 0.42/0.72 (define @t42 () (@var "C" tptp.term)) % 0.42/0.72 (define @t43 () (_ @t8 @t42)) % 0.42/0.72 (define @t44 () (= @t43 @t41)) % 0.42/0.72 (define @t45 () (@list @t5 @t2 @t42 @t39)) % 0.42/0.72 (define @t46 () (= @t42 @t39)) % 0.42/0.72 (define @t47 () (forall @t45 (=> @t44 @t46))) % 0.42/0.72 (define @t48 () (= tptp.apinj2 @t47)) % 0.42/0.72 (define @t49 () (@list @t5 @t2)) % 0.42/0.72 (define @t50 () (forall @t14 @t35)) % 0.42/0.72 (define @t51 () (_ @t34 @t18)) % 0.42/0.72 (define @t52 () (_ @t34 @t2)) % 0.42/0.72 (define @t53 () (forall @t49 (=> @t35 (=> @t52 (_ @t34 @t9))))) % 0.42/0.72 (define @t54 () (@var "Q" (-> tptp.term Bool))) % 0.42/0.72 (define @t55 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t34) @t54)) % 0.42/0.72 (define @t56 () (@list @t54)) % 0.42/0.72 (define @t57 () (@list @t34 @t5 @t1)) % 0.42/0.72 (define @t58 () (_ tptp.push @t2)) % 0.42/0.72 (define @t59 () (@var "K" (-> tptp.term Bool))) % 0.42/0.72 (define @t60 () (@list @t34 @t54 @t5 @t1)) % 0.42/0.72 (define @t61 () (_ tptp.sub @t42)) % 0.42/0.72 (define @t62 () (@list @t42)) % 0.42/0.72 (define @t63 () (_ tptp.var @t2)) % 0.42/0.72 (define @t64 () (@list @t2)) % 0.42/0.72 (define @t65 () (forall @t64 (=> @t63 (_ @t34 @t4)))) % 0.42/0.72 (define @t66 () (_ @t3 @t10)) % 0.42/0.72 (define @t67 () (forall @t64 (=> @t63 (_ @t34 @t66)))) % 0.42/0.72 (define @t68 () (_ @t54 @t2)) % 0.42/0.72 (define @t69 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.42/0.72 (define @t70 () (_ @t6 (_ @t58 tptp.id))) % 0.42/0.72 (define @t71 () (forall @t14 (=> (forall @t64 (=> @t52 (_ @t34 @t70))) @t51))) % 0.42/0.72 (define @t72 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.42/0.72 (define @t73 () (=> tptp.induction2lem tptp.induction2)) % 0.42/0.72 (define @t74 () (_ tptp.hoasap tptp.id)) % 0.42/0.72 (define @t75 () (_ (_ @t74 @t5) tptp.id)) % 0.42/0.72 (define @t76 () (= (_ @t75 @t42) (_ (_ (_ @t74 @t2) tptp.id) @t39))) % 0.42/0.72 (define @t77 () (=> @t76 @t46)) % 0.42/0.72 (define @t78 () (forall @t45 @t77)) % 0.42/0.72 (define @t79 () (= tptp.hoasapinj2 @t78)) % 0.42/0.72 (define @t80 () (=> tptp.apinj2 tptp.hoasapinj2)) % 0.42/0.72 (define @t81 () (= tptp.hoasapinj2_lthm @t80)) % 0.42/0.72 (define @t82 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.42/0.72 (define @t83 () (_ (_ @t82 @t1) @t5)) % 0.42/0.72 (define @t84 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.42/0.72 (define @t85 () (_ @t84 @t1)) % 0.42/0.72 (define @t86 () (_ @t85 @t5)) % 0.42/0.72 (define @t87 () (@list @t1 @t5)) % 0.42/0.72 (define @t88 () (_ tptp.hoaslam tptp.id)) % 0.42/0.72 (define @t89 () (_ @t88 (lambda @t87 @t86))) % 0.42/0.72 (define @t90 () (@list @t1 @t5 @t19)) % 0.42/0.72 (define @t91 () (_ (_ @t84 @t20) @t28)) % 0.42/0.72 (define @t92 () (_ (_ tptp.sub @t86) @t19)) % 0.42/0.72 (define @t93 () (forall @t90 (= @t92 @t91))) % 0.42/0.72 (define @t94 () (@list @t84)) % 0.42/0.72 (define @t95 () (_ @t75 @t2)) % 0.42/0.72 (define @t96 () (_ tptp.hoasvar tptp.id)) % 0.42/0.72 (define @t97 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.42/0.72 (define @t98 () (_ (_ tptp.hoasinduction_p_and_p_prime @t97) @t54)) % 0.42/0.72 (define @t99 () (@list @t97)) % 0.42/0.72 (define @t100 () (_ @t54 @t5)) % 0.42/0.72 (define @t101 () (_ @t97 tptp.id)) % 0.42/0.72 (define @t102 () (_ (_ @t101 @t5) tptp.id)) % 0.42/0.72 (define @t103 () (forall @t14 (=> (_ (_ @t96 @t5) tptp.id) @t102))) % 0.42/0.72 (define @t104 () (_ (_ (_ @t97 @t1) @t5) (_ (_ tptp.comp @t26) @t19))) % 0.42/0.72 (define @t105 () (_ (_ (_ @t97 (_ @t16 @t26)) (_ @t6 @t26)) @t19)) % 0.42/0.72 (define @t106 () (@list @t1 @t5 @t19 @t26)) % 0.42/0.72 (define @t107 () (forall @t106 (=> @t105 @t104))) % 0.42/0.72 (define @t108 () (forall @t106 (=> @t104 @t105))) % 0.42/0.72 (define @t109 () (@list @t97 @t54)) % 0.42/0.72 (define @t110 () (_ (_ @t101 @t2) tptp.id)) % 0.42/0.72 (define @t111 () (forall @t49 (=> @t102 (=> @t110 (_ (_ @t101 @t95) tptp.id))))) % 0.42/0.72 (define @t112 () (=> (forall @t14 (=> @t102 (_ (_ @t101 (_ (_ @t84 tptp.id) @t5)) tptp.id))) (_ (_ @t101 @t89) tptp.id))) % 0.42/0.72 (define @t113 () (forall @t94 (=> @t93 @t112))) % 0.42/0.72 (define @t114 () (=> @t113 (=> @t98 (forall @t14 (=> (forall @t64 (=> @t68 (_ @t54 @t70))) (_ @t54 @t18)))))) % 0.42/0.72 (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))))))))))))))))))))))))))))))))))) % 0.42/0.72 (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))))))))))))))))))))))))))))))))))) % 0.42/0.72 (define @t117 () (forall @t64 (=> @t110 (_ (_ @t101 @t70) tptp.id)))) % 0.42/0.72 (define @t118 () (forall @t14 (=> @t117 (_ (_ @t101 (_ tptp.lam (_ @t6 @t31))) tptp.id)))) % 0.42/0.72 (define @t119 () (=> @t113 (forall @t14 (=> @t117 (_ (_ @t101 @t18) tptp.id))))) % 0.42/0.72 (define @t120 () (_ (_ @t84 tptp.sh) tptp.one)) % 0.42/0.72 (define @t121 () (=> @t111 (=> @t113 (forall @t14 @t102)))) % 0.42/0.72 (define @t122 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.42/0.72 (define @t123 () (not tptp.hoasapinj2_lthm)) % 0.42/0.72 (define @t124 () (@var "X" tptp.term)) % 0.42/0.72 (define @t125 () (_ @t54 @t124)) % 0.42/0.72 (define @t126 () (@list @t124)) % 0.42/0.72 (define @t127 () (lambda (@list @t5 @t1 @t34 @t54) (forall @t126 (= @t125 (_ @t34 (_ (_ tptp.sub @t124) @t10)))))) % 0.42/0.72 (define @t128 () (_ tptp.ap @t28)) % 0.42/0.72 (define @t129 () (_ @t128 @t2)) % 0.42/0.72 (define @t130 () (lambda (@list @t1 @t5 @t19 @t2) @t129)) % 0.42/0.72 (define @t131 () (lambda (@list @t1 @t84) (_ tptp.lam @t120))) % 0.42/0.72 (define @t132 () (lambda @t90 (_ tptp.var @t28))) % 0.42/0.72 (define @t133 () (lambda @t109 (forall @t126 (= @t125 (_ (_ @t101 @t124) tptp.id))))) % 0.42/0.72 (define @t134 () (_ @t3 tptp.id)) % 0.42/0.72 (define @t135 () (tptp.sub @t2 tptp.id)) % 0.42/0.72 (define @t136 () (tptp.ap @t135 @t39)) % 0.42/0.72 (define @t137 () (_ tptp.ap @t134)) % 0.42/0.72 (define @t138 () (_ @t137 @t39)) % 0.42/0.72 (define @t139 () (tptp.sub @t5 tptp.id)) % 0.42/0.72 (define @t140 () (tptp.ap @t139 @t42)) % 0.42/0.72 (define @t141 () (_ tptp.ap @t13)) % 0.42/0.72 (define @t142 () (_ @t141 @t42)) % 0.42/0.72 (define @t143 () (= @t142 @t138)) % 0.42/0.72 (define @t144 () (not @t143)) % 0.42/0.72 (define @t145 () (or @t144 @t46)) % 0.42/0.72 (define @t146 () (@var "BOUND_VARIABLE_9440" tptp.term)) % 0.42/0.72 (define @t147 () (lambda (@list @t146) (_ @t137 @t146))) % 0.42/0.72 (define @t148 () (lambda (@list @t19 @t146) (_ (_ tptp.ap (_ @t3 @t19)) @t146))) % 0.42/0.72 (define @t149 () (lambda (@list @t5 @t19 @t2) @t129)) % 0.42/0.72 (define @t150 () (_ @t130 tptp.id)) % 0.42/0.72 (define @t151 () (lambda @t64 (_ @t141 @t2))) % 0.42/0.72 (define @t152 () (lambda (@list @t19 @t2) @t129)) % 0.42/0.72 (define @t153 () (= (_ (_ (_ @t150 @t5) tptp.id) @t42) (_ (_ (_ @t150 @t2) tptp.id) @t39))) % 0.42/0.72 (define @t154 () (=> @t153 @t46)) % 0.42/0.72 (define @t155 () (forall @t45 @t154)) % 0.42/0.72 (define @t156 () (tptp.ap @t2 @t39)) % 0.42/0.72 (define @t157 () (tptp.ap @t5 @t42)) % 0.42/0.72 (define @t158 () (not @t44)) % 0.42/0.72 (define @t159 () (or @t158 @t46)) % 0.42/0.72 (define @t160 () (forall @t45 (or (not (= @t157 @t156)) @t46))) % 0.42/0.72 (define @t161 () (forall @t45 (or (not (= @t140 @t136)) @t46))) % 0.42/0.72 (define @t162 () (@quantifiers_skolemize @t161 3)) % 0.42/0.72 (define @t163 () (@quantifiers_skolemize @t161 2)) % 0.42/0.72 (define @t164 () (tptp.sub (@quantifiers_skolemize @t161 1) tptp.id)) % 0.42/0.72 (define @t165 () (tptp.sub (@quantifiers_skolemize @t161 0) tptp.id)) % 0.42/0.72 (define @t166 () (or (not (= (tptp.ap @t165 @t163) (tptp.ap @t164 @t162))) (= @t163 @t162))) % 0.42/0.72 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.42/0.72 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.42/0.72 (assume @p3 (= tptp.axvarid @t15)) % 0.42/0.72 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t18) @t1) (_ tptp.lam (_ @t6 (_ @t17 (_ @t16 tptp.sh)))))))) % 0.42/0.72 (assume @p5 (= tptp.axclos @t22)) % 0.42/0.72 (assume @p6 (= tptp.axidl @t24)) % 0.42/0.72 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t25 @t10) @t1)))) % 0.42/0.72 (assume @p8 (= tptp.axassoc @t27)) % 0.42/0.72 (assume @p9 (= tptp.axmap (forall @t21 (= (_ (_ tptp.comp @t10) @t19) @t29)))) % 0.42/0.72 (assume @p10 (= tptp.axidr @t30)) % 0.42/0.72 (assume @p11 (= tptp.axvarshift (= @t31 tptp.id))) % 0.42/0.72 (assume @p12 (= tptp.axscons (forall @t23 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t25 @t1)) @t1)))) % 0.42/0.72 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.42/0.72 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t33 (_ tptp.var @t32))))) % 0.42/0.72 (assume @p15 (= tptp.ulamvarind (forall @t37 (=> (_ @t34 tptp.one) (=> (forall @t14 (=> @t33 (=> @t35 (_ @t34 @t32)))) @t36))))) % 0.42/0.72 (assume @p16 (= tptp.apinj1 (forall @t45 (=> @t44 @t38)))) % 0.42/0.72 (assume @p17 @t48) % 0.42/0.72 (assume @p18 (= tptp.laminj (forall @t49 (=> (= @t18 (_ tptp.lam @t2)) @t38)))) % 0.42/0.72 (assume @p19 (= tptp.shinj (forall @t49 (=> (= @t32 (_ @t3 tptp.sh)) @t38)))) % 0.42/0.72 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t42) (not (= @t18 (_ @t40 @t42)))))) % 0.42/0.72 (assume @p21 (= tptp.apnotvar (forall @t49 (not (_ tptp.var @t9))))) % 0.42/0.72 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t18))))) % 0.42/0.72 (assume @p23 (= tptp.induction (forall @t37 (=> @t36 (=> @t53 (=> (forall @t14 (=> @t35 @t51)) @t50)))))) % 0.42/0.72 (assume @p24 (= tptp.pushprop_lem0 (forall @t57 (exists @t56 @t55)))) % 0.42/0.72 (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))))))))))))))))))))))))) % 0.42/0.72 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.42/0.72 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t34 @t59 @t5 @t1 @t2) (=> @t35 (_ @t59 (_ @t6 (_ @t58 @t1))))))) % 0.42/0.72 (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))))))))))))))))))))))))) % 0.42/0.72 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.42/0.72 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t60 (=> @t35 (=> @t55 (_ @t54 tptp.one)))))) % 0.42/0.72 (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))))))))))))))))))))))))) % 0.42/0.72 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.42/0.72 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t60 (=> @t55 (=> @t65 (forall @t62 (=> (_ tptp.var @t42) (=> (_ @t54 @t42) (_ @t54 (_ @t61 tptp.sh)))))))))) % 0.42/0.72 (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))))))))))))))))))))))))) % 0.42/0.72 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.42/0.72 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t60 (=> @t55 (=> (forall @t64 (=> @t63 @t68)) @t67))))) % 0.42/0.72 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.42/0.72 (assume @p38 (= tptp.pushprop (forall @t57 (=> @t65 (=> @t35 @t67))))) % 0.42/0.72 (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))))))))))))))))))))))))) % 0.42/0.72 (assume @p40 (= tptp.pushprop_lthm_orig @t69)) % 0.42/0.72 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t69))) % 0.42/0.72 (assume @p42 (= tptp.induction2lem (forall @t37 (=> @t53 (=> @t71 (forall @t12 (=> @t65 (_ @t34 @t7)))))))) % 0.42/0.72 (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 @t72)))))))))))))))))))))))) % 0.42/0.72 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t72)))))))))) % 0.42/0.72 (assume @p45 (= tptp.induction2 (forall @t37 (=> @t36 (=> @t53 (=> @t71 @t50)))))) % 0.42/0.72 (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 @t73)))))))))))))))))))))))))) % 0.42/0.72 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t73))) % 0.42/0.72 (assume @p48 (= tptp.substmonoid (and @t27 @t24 @t30))) % 0.42/0.72 (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)))))))))))))))))))))))))))) % 0.42/0.72 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.42/0.72 (assume @p51 (= tptp.termmset (and @t22 @t15))) % 0.42/0.72 (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))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.42/0.72 (assume @p54 (= tptp.hoasapinj1 (forall @t45 (=> @t76 @t38)))) % 0.42/0.72 (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)))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.42/0.72 (assume @p57 @t79) % 0.42/0.72 (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))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p59 @t81) % 0.42/0.72 (assume @p60 (= tptp.hoaslaminj (forall @t94 (=> @t93 (forall (@list @t82) (=> (forall @t90 (= (_ (_ tptp.sub @t83) @t19) (_ (_ @t82 @t20) @t28))) (=> (= @t89 (_ @t88 (lambda @t87 @t83))) (forall @t87 (= @t86 @t83))))))))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.42/0.72 (assume @p63 (= tptp.hoaslamnotap (forall @t94 (=> @t93 (forall @t49 (not (= (_ @t88 (lambda (@list @t1 @t42) (_ @t85 @t42))) @t95))))))) % 0.42/0.72 (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))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.42/0.72 (assume @p66 (= tptp.hoaslamnotvar (forall @t94 (=> @t93 (not (_ (_ @t96 @t89) tptp.id)))))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.42/0.72 (assume @p69 (= tptp.hoasapnotvar (forall @t49 (not (_ (_ @t96 @t95) tptp.id))))) % 0.42/0.72 (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))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.42/0.72 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t99 (exists @t56 @t98)))) % 0.42/0.72 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.42/0.72 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t109 (=> @t108 (=> @t107 (=> @t103 (=> @t98 (forall @t14 (=> @t33 @t100))))))))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t109 (=> @t108 (=> @t107 (=> @t111 (=> @t98 (forall @t49 (=> @t100 (=> @t68 (_ @t54 @t9))))))))))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t64 (exists @t94 (forall @t12 (= @t86 @t66)))))) % 0.42/0.72 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.42/0.72 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t109 (=> @t108 (=> @t107 @t114))))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.42/0.72 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t109 @t114))) % 0.42/0.72 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.42/0.72 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t99 (=> @t108 (=> @t107 (=> @t103 (forall @t14 (=> @t33 @t102)))))))) % 0.42/0.72 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t115)) % 0.42/0.72 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t115)) % 0.42/0.72 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t99 (=> @t108 (=> @t107 (=> @t111 (forall @t49 (=> @t102 (=> @t110 (_ (_ @t101 @t9) tptp.id)))))))))) % 0.42/0.72 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t116)) % 0.42/0.72 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t116)) % 0.42/0.72 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t99 (=> @t113 @t118)))) % 0.42/0.72 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.42/0.72 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t99 (=> (forall @t94 (=> (exists @t62 (forall @t90 (and (= @t92 (_ (_ tptp.sub (_ @t61 @t10)) @t19)) (= (_ @t61 @t29) @t91)))) @t112)) @t118)))) % 0.42/0.72 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t99 (=> @t108 (=> @t107 @t119))))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.42/0.72 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t99 @t119))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.42/0.72 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t64 (exists @t94 (= (_ @t3 @t31) @t120))))) % 0.42/0.72 (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)))))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.42/0.72 (assume @p103 (= tptp.hoasinduction (forall @t99 (=> @t108 (=> @t107 (=> @t103 @t121)))))) % 0.42/0.72 (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 @t122)))))))))))))))))))))))))))))))))))) % 0.42/0.72 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t122))) % 0.42/0.72 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.42/0.72 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t99 @t121))) % 0.42/0.72 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.42/0.72 (assume @p109 @t123) % 0.42/0.72 (assume @p110 true) % 0.42/0.72 (step @p111 (= tptp.pushprop_p_and_p_prime @t127) :rule refl :args (@t127)) % 0.42/0.72 (step @p112 (= tptp.hoasap @t130) :rule refl :args (@t130)) % 0.42/0.72 (step @p113 (= tptp.hoaslam @t131) :rule refl :args (@t131)) % 0.42/0.72 (step @p114 (= tptp.hoasvar @t132) :rule refl :args (@t132)) % 0.42/0.72 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t133) :rule refl :args (@t133)) % 0.42/0.72 (step @p116 :rule refl :args (@t46)) % 0.42/0.72 (step @p117 :rule refl :args ((tptp.ap @t134 @t39))) % 0.42/0.72 (step @p118 :rule refl :args (@t39)) % 0.42/0.72 (step @p119 :rule refl :args (@t135)) % 0.42/0.72 (step @p120 :rule cong :premises (@p119 @p118) :args (@t136)) % 0.42/0.72 (step @p121 :rule trans :premises (@p120 @p117)) % 0.42/0.72 (step @p122 :rule refl :args (tptp.ap)) % 0.42/0.72 (step @p123 :rule ho_cong :premises (@p122 @p119)) % 0.42/0.72 (step @p124 :rule ho_cong :premises (@p123 @p118)) % 0.42/0.72 (step @p125 :rule cong :premises (@p124 @p121) :args ((= (_ (_ tptp.ap @t135) @t39) @t136))) % 0.42/0.72 (step @p126 :rule symm :premises (@p125)) % 0.42/0.72 (step @p127 :rule refl :args (@t138)) % 0.42/0.72 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 0.42/0.72 (step @p129 :rule refl :args (@t134)) % 0.42/0.72 (step @p130 :rule cong :premises (@p129 @p119) :args ((= @t134 @t135))) % 0.42/0.72 (step @p131 :rule symm :premises (@p130)) % 0.42/0.72 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 0.42/0.72 (step @p133 :rule ho_cong :premises (@p122 @p132)) % 0.42/0.72 (step @p134 :rule ho_cong :premises (@p133 @p118)) % 0.42/0.72 (step @p135 :rule trans :premises (@p134 @p128)) % 0.42/0.72 (step @p136 :rule refl :args ((tptp.ap @t13 @t42))) % 0.42/0.72 (step @p137 :rule refl :args (@t42)) % 0.42/0.72 (step @p138 :rule refl :args (@t139)) % 0.42/0.72 (step @p139 :rule cong :premises (@p138 @p137) :args (@t140)) % 0.42/0.72 (step @p140 :rule trans :premises (@p139 @p136)) % 0.42/0.72 (step @p141 :rule ho_cong :premises (@p122 @p138)) % 0.42/0.72 (step @p142 :rule ho_cong :premises (@p141 @p137)) % 0.42/0.72 (step @p143 :rule cong :premises (@p142 @p140) :args ((= (_ (_ tptp.ap @t139) @t42) @t140))) % 0.42/0.72 (step @p144 :rule symm :premises (@p143)) % 0.42/0.72 (step @p145 :rule refl :args (@t142)) % 0.42/0.72 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 0.42/0.72 (step @p147 :rule refl :args (@t13)) % 0.42/0.72 (step @p148 :rule cong :premises (@p147 @p138) :args ((= @t13 @t139))) % 0.42/0.72 (step @p149 :rule symm :premises (@p148)) % 0.42/0.72 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 0.42/0.72 (step @p151 :rule ho_cong :premises (@p122 @p150)) % 0.42/0.72 (step @p152 :rule ho_cong :premises (@p151 @p137)) % 0.42/0.72 (step @p153 :rule trans :premises (@p152 @p146)) % 0.42/0.72 (step @p154 :rule cong :premises (@p153 @p135) :args (@t143)) % 0.42/0.72 (step @p155 :rule cong :premises (@p154) :args (@t144)) % 0.42/0.72 (step @p156 :rule nary_cong :premises (@p155 @p116) :args (@t145)) % 0.42/0.72 (step @p157 :rule cong :premises (@p156) :args ((forall @t45 @t145))) % 0.42/0.72 (step @p158 :rule bool-impl-elim :args (@t143 @t46)) % 0.42/0.72 (step @p159 :rule cong :premises (@p158) :args ((forall @t45 (=> @t143 @t46)))) % 0.42/0.72 (step @p160 :rule trans :premises (@p159 @p157)) % 0.42/0.72 (step @p161 :rule refl :args (@t46)) % 0.42/0.72 (step @p162 :rule beta-reduce :args ((= (_ @t147 @t39) @t138))) % 0.42/0.72 (step @p163 :rule refl :args (@t39)) % 0.42/0.72 (step @p164 :rule beta-reduce :args ((= (_ @t148 tptp.id) @t147))) % 0.42/0.72 (step @p165 :rule refl :args (tptp.id)) % 0.42/0.72 (step @p166 :rule beta-reduce :args ((= (_ (lambda (@list @t5 @t19 @t146) (_ @t128 @t146)) @t2) @t148))) % 0.42/0.72 (step @p167 :rule refl :args (@t2)) % 0.42/0.72 (step @p168 :rule alpha_equiv :args (@t149 (@list @t2) (@list @t146))) % 0.42/0.72 (step @p169 :rule ho_cong :premises (@p168 @p167)) % 0.42/0.72 (step @p170 :rule trans :premises (@p169 @p166)) % 0.42/0.72 (step @p171 :rule refl :args (@t2)) % 0.42/0.72 (step @p172 :rule beta-reduce :args ((= @t150 @t149))) % 0.42/0.72 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 0.42/0.72 (step @p174 :rule trans :premises (@p173 @p170)) % 0.42/0.72 (step @p175 :rule ho_cong :premises (@p174 @p165)) % 0.42/0.72 (step @p176 :rule trans :premises (@p175 @p164)) % 0.42/0.72 (step @p177 :rule ho_cong :premises (@p176 @p163)) % 0.42/0.72 (step @p178 :rule trans :premises (@p177 @p162)) % 0.42/0.72 (step @p179 :rule beta-reduce :args ((= (_ @t151 @t42) @t142))) % 0.42/0.72 (step @p180 :rule refl :args (@t42)) % 0.42/0.72 (step @p181 :rule beta-reduce :args ((= (_ @t152 tptp.id) @t151))) % 0.42/0.72 (step @p182 :rule beta-reduce :args ((= (_ @t149 @t5) @t152))) % 0.42/0.72 (step @p183 :rule refl :args (@t5)) % 0.42/0.72 (step @p184 :rule ho_cong :premises (@p172 @p183)) % 0.42/0.72 (step @p185 :rule trans :premises (@p184 @p182)) % 0.42/0.72 (step @p186 :rule ho_cong :premises (@p185 @p165)) % 0.42/0.72 (step @p187 :rule trans :premises (@p186 @p181)) % 0.42/0.72 (step @p188 :rule ho_cong :premises (@p187 @p180)) % 0.42/0.72 (step @p189 :rule trans :premises (@p188 @p179)) % 0.42/0.72 (step @p190 :rule cong :premises (@p189 @p178) :args (@t153)) % 0.42/0.72 (step @p191 :rule cong :premises (@p190 @p161) :args (@t154)) % 0.42/0.72 (step @p192 :rule cong :premises (@p191) :args (@t155)) % 0.42/0.72 (step @p193 :rule trans :premises (@p192 @p160)) % 0.42/0.72 (step @p194 :rule refl :args (tptp.hoasapinj2)) % 0.42/0.72 (step @p195 :rule cong :premises (@p194 @p193) :args ((= tptp.hoasapinj2 @t155))) % 0.42/0.72 (step @p196 :rule ho_cong :premises (@p112 @p165)) % 0.42/0.72 (step @p197 :rule ho_cong :premises (@p196 @p171)) % 0.42/0.72 (step @p198 :rule ho_cong :premises (@p197 @p165)) % 0.42/0.72 (step @p199 :rule ho_cong :premises (@p198 @p163)) % 0.42/0.72 (step @p200 :rule ho_cong :premises (@p196 @p183)) % 0.42/0.72 (step @p201 :rule ho_cong :premises (@p200 @p165)) % 0.42/0.72 (step @p202 :rule ho_cong :premises (@p201 @p180)) % 0.42/0.72 (step @p203 :rule cong :premises (@p202 @p199) :args (@t76)) % 0.42/0.72 (step @p204 :rule cong :premises (@p203 @p161) :args (@t77)) % 0.42/0.72 (step @p205 :rule cong :premises (@p204) :args (@t78)) % 0.42/0.72 (step @p206 :rule cong :premises (@p194 @p205) :args (@t79)) % 0.42/0.72 (step @p207 :rule trans :premises (@p206 @p195)) % 0.42/0.72 (step @p208 :rule eq_resolve :premises (@p57 @p207)) % 0.42/0.72 (step @p209 :rule refl :args (@t156)) % 0.42/0.72 (step @p210 :rule refl :args (@t41)) % 0.42/0.72 (step @p211 :rule cong :premises (@p210 @p209) :args ((= @t41 @t156))) % 0.42/0.72 (step @p212 :rule symm :premises (@p211)) % 0.42/0.72 (step @p213 :rule eq_resolve :premises (@p210 @p212)) % 0.42/0.72 (step @p214 :rule refl :args (@t157)) % 0.42/0.72 (step @p215 :rule refl :args (@t43)) % 0.42/0.72 (step @p216 :rule cong :premises (@p215 @p214) :args ((= @t43 @t157))) % 0.42/0.72 (step @p217 :rule symm :premises (@p216)) % 0.42/0.72 (step @p218 :rule eq_resolve :premises (@p215 @p217)) % 0.42/0.72 (step @p219 :rule cong :premises (@p218 @p213) :args (@t44)) % 0.42/0.72 (step @p220 :rule cong :premises (@p219) :args (@t158)) % 0.42/0.72 (step @p221 :rule nary_cong :premises (@p220 @p116) :args (@t159)) % 0.42/0.72 (step @p222 :rule cong :premises (@p221) :args ((forall @t45 @t159))) % 0.42/0.72 (step @p223 :rule bool-impl-elim :args (@t44 @t46)) % 0.42/0.72 (step @p224 :rule cong :premises (@p223) :args (@t47)) % 0.42/0.72 (step @p225 :rule trans :premises (@p224 @p222)) % 0.42/0.72 (step @p226 :rule refl :args (tptp.apinj2)) % 0.42/0.72 (step @p227 :rule cong :premises (@p226 @p225) :args (@t48)) % 0.42/0.72 (step @p228 :rule eq_resolve :premises (@p17 @p227)) % 0.42/0.72 (step @p229 :rule cong :premises (@p228 @p208) :args (@t80)) % 0.42/0.72 (step @p230 :rule refl :args (tptp.hoasapinj2_lthm)) % 0.42/0.72 (step @p231 :rule cong :premises (@p230 @p229) :args (@t81)) % 0.42/0.72 (step @p232 :rule eq_resolve :premises (@p59 @p231)) % 0.42/0.72 (step @p233 :rule cong :premises (@p232) :args (@t123)) % 0.42/0.72 (step @p234 :rule eq_resolve :premises (@p109 @p233)) % 0.42/0.72 (step @p235 :rule not_implies_elim1 :premises (@p234)) % 0.42/0.72 (step @p236 :rule not_implies_elim2 :premises (@p234)) % 0.42/0.72 (step @p237 :rule skolemize :premises (@p236)) % 0.42/0.72 (assume-push @p244 @t160) % 0.42/0.72 (step @p239 :rule instantiate :premises (@p235) :args ((@list @t165 @t164 @t163 @t162))) % 0.42/0.72 (step-pop @p245 :rule scope :premises (@p239)) % 0.42/0.72 (step @p240 :rule process_scope :premises (@p245) :args (@t166)) % 0.42/0.72 (step @p242 :rule implies_elim :premises (@p240)) % 0.42/0.72 (step @p243 false :rule chain_m_resolution :premises (@p242 @p237 @p235) :args (false (@list true false) (@list @t166 @t160))) % 0.42/0.72 ) % 0.42/0.72 % SZS output end Proof % 0.42/0.72 % cvc5 exiting %------------------------------------------------------------------------------