%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG256^2 : 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 : n025.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 0.41s 0.75s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG256^2 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n025.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 01:55:01 EDT 2026 % 0.16/0.34 % CPUTime : % 0.39/0.57 %----Proving TH0 % 0.41/0.75 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.75 % SZS status Theorem % 0.41/0.75 % SZS output start Proof % 0.41/0.75 ( % 0.41/0.75 (declare-sort tptp.term 0) % 0.41/0.75 (declare-sort tptp.subst 0) % 0.41/0.75 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.41/0.75 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.41/0.75 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.41/0.75 (declare-const tptp.one tptp.term) % 0.41/0.75 (declare-const tptp.sh tptp.subst) % 0.41/0.75 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.41/0.75 (declare-const tptp.var (-> tptp.term Bool)) % 0.41/0.75 (declare-const tptp.id tptp.subst) % 0.41/0.75 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3b Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3a Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3 Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem2 Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem1 Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasinduction_lem0 Bool) % 0.41/0.75 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasapnotvar Bool) % 0.41/0.75 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.41/0.75 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.41/0.75 (declare-const tptp.hoaslamnotvar Bool) % 0.41/0.75 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.41/0.75 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.41/0.75 (declare-const tptp.hoaslamnotap Bool) % 0.41/0.75 (declare-const tptp.hoaslaminj_lthm Bool) % 0.41/0.75 (declare-const tptp.hoaslaminj_gthm Bool) % 0.41/0.75 (declare-const tptp.hoaslaminj Bool) % 0.41/0.75 (declare-const tptp.hoasapinj2_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasapinj2_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasapinj2 Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.41/0.75 (declare-const tptp.axassoc Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.41/0.75 (declare-const tptp.axvarcons Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem0 Bool) % 0.41/0.75 (declare-const tptp.apinj1 Bool) % 0.41/0.75 (declare-const tptp.induction Bool) % 0.41/0.75 (declare-const tptp.apnotvar Bool) % 0.41/0.75 (declare-const tptp.laminj Bool) % 0.41/0.75 (declare-const tptp.axvarshift Bool) % 0.41/0.75 (declare-const tptp.ulamvarind Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.41/0.75 (declare-const tptp.ulamvarsh Bool) % 0.41/0.75 (declare-const tptp.ulamvar1 Bool) % 0.41/0.75 (declare-const tptp.axabs Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem1 Bool) % 0.41/0.75 (declare-const tptp.shinj Bool) % 0.41/0.75 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.41/0.75 (declare-const tptp.apinj2 Bool) % 0.41/0.75 (declare-const tptp.axvarid Bool) % 0.41/0.75 (declare-const tptp.axidl Bool) % 0.41/0.75 (declare-const tptp.axclos Bool) % 0.41/0.75 (declare-const tptp.termmset Bool) % 0.41/0.75 (declare-const tptp.axshiftcons Bool) % 0.41/0.75 (declare-const tptp.lamnotap Bool) % 0.41/0.75 (declare-const tptp.lamnotvar Bool) % 0.41/0.75 (declare-const tptp.axapp Bool) % 0.41/0.75 (declare-const tptp.axscons Bool) % 0.41/0.75 (declare-const tptp.axmap Bool) % 0.41/0.75 (declare-const tptp.axidr Bool) % 0.41/0.75 (declare-const tptp.induction2lem Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasapinj1_lthm Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem1v2 Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.41/0.75 (declare-const tptp.induction2 Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem2v2 Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem3v2 Bool) % 0.41/0.75 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.41/0.75 (declare-const tptp.pushprop Bool) % 0.41/0.75 (declare-const tptp.pushprop_gthm Bool) % 0.41/0.75 (declare-const tptp.hoasapinj1 Bool) % 0.41/0.75 (declare-const tptp.pushprop_lthm_orig Bool) % 0.41/0.75 (declare-const tptp.pushprop_lthm Bool) % 0.41/0.75 (declare-const tptp.induction2lem_gthm Bool) % 0.41/0.75 (declare-const tptp.induction2lem_lthm Bool) % 0.41/0.75 (declare-const tptp.induction2_gthm Bool) % 0.41/0.75 (declare-const tptp.induction2_lthm Bool) % 0.41/0.75 (declare-const tptp.substmonoid Bool) % 0.41/0.75 (declare-const tptp.substmonoid_gthm Bool) % 0.41/0.75 (declare-const tptp.termmset_gthm Bool) % 0.41/0.75 (declare-const tptp.substmonoid_lthm Bool) % 0.41/0.75 (declare-const tptp.termmset_lthm Bool) % 0.41/0.75 (declare-const tptp.hoasapinj1_gthm Bool) % 0.41/0.75 (define tptp.pushprop_p_and_p_prime () (let ((_let_1 (@var "M" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (let ((_let_3 (@var "X" tptp.term))) (let ((_let_4 (@var "P" (-> tptp.term Bool)))) (let ((_let_5 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_1 _let_4 _let_5) (forall (@list _let_3) (= (_ _let_5 _let_3) (_ _let_4 (_ (_ tptp.sub _let_3) (_ (_ tptp.push _let_2) _let_1)))))))))))) % 0.41/0.75 (define tptp.hoasap () (let ((_let_1 (@var "B" tptp.term))) (let ((_let_2 (@var "N" tptp.subst))) (let ((_let_3 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_3 _let_2 _let_1) (_ (_ tptp.ap (_ (_ tptp.sub _let_3) _let_2)) _let_1)))))) % 0.41/0.75 (define tptp.hoaslam () (let ((_let_1 (@var "F" (-> tptp.subst tptp.term tptp.term)))) (lambda (@list (@var "M" tptp.subst) _let_1) (_ tptp.lam (_ (_ _let_1 tptp.sh) tptp.one))))) % 0.41/0.75 (define tptp.hoasvar () (let ((_let_1 (@var "N" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_2 _let_1) (_ tptp.var (_ (_ tptp.sub _let_2) _let_1)))))) % 0.41/0.75 (define tptp.hoasinduction_p_and_p_prime () (let ((_let_1 (@var "X" tptp.term))) (let ((_let_2 (@var "P" (-> tptp.subst tptp.term tptp.subst Bool)))) (let ((_let_3 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (= (_ _let_3 _let_1) (_ (_ (_ _let_2 tptp.id) _let_1) tptp.id)))))))) % 0.41/0.75 (define @t1 () (@var "M" tptp.subst)) % 0.41/0.75 (define @t2 () (@var "B" tptp.term)) % 0.41/0.75 (define @t3 () (_ tptp.sub @t2)) % 0.41/0.75 (define @t4 () (_ @t3 @t1)) % 0.41/0.75 (define @t5 () (@var "A" tptp.term)) % 0.41/0.75 (define @t6 () (_ tptp.sub @t5)) % 0.41/0.75 (define @t7 () (_ @t6 @t1)) % 0.41/0.75 (define @t8 () (_ tptp.ap @t5)) % 0.41/0.75 (define @t9 () (_ @t8 @t2)) % 0.41/0.75 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 0.41/0.75 (define @t11 () (_ tptp.sub tptp.one)) % 0.41/0.75 (define @t12 () (@list @t5 @t1)) % 0.41/0.75 (define @t13 () (_ @t6 tptp.id)) % 0.41/0.75 (define @t14 () (@list @t5)) % 0.41/0.75 (define @t15 () (forall @t14 (= @t13 @t5))) % 0.41/0.75 (define @t16 () (= tptp.axvarid @t15)) % 0.41/0.75 (define @t17 () (_ tptp.comp @t1)) % 0.41/0.75 (define @t18 () (_ tptp.push tptp.one)) % 0.41/0.75 (define @t19 () (_ tptp.lam @t5)) % 0.41/0.75 (define @t20 () (@var "N" tptp.subst)) % 0.41/0.75 (define @t21 () (_ @t17 @t20)) % 0.41/0.75 (define @t22 () (@list @t5 @t1 @t20)) % 0.41/0.75 (define @t23 () (forall @t22 (= (_ (_ tptp.sub @t7) @t20) (_ @t6 @t21)))) % 0.41/0.75 (define @t24 () (@list @t1)) % 0.41/0.75 (define @t25 () (forall @t24 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 0.41/0.75 (define @t26 () (_ tptp.comp tptp.sh)) % 0.41/0.75 (define @t27 () (@var "K" tptp.subst)) % 0.41/0.75 (define @t28 () (forall (@list @t1 @t20 @t27) (= (_ (_ tptp.comp @t21) @t27) (_ @t17 (_ (_ tptp.comp @t20) @t27))))) % 0.41/0.75 (define @t29 () (_ @t6 @t20)) % 0.41/0.75 (define @t30 () (_ (_ tptp.push @t29) @t21)) % 0.41/0.75 (define @t31 () (forall @t24 (= (_ @t17 tptp.id) @t1))) % 0.41/0.75 (define @t32 () (_ @t18 tptp.sh)) % 0.41/0.75 (define @t33 () (_ @t6 tptp.sh)) % 0.41/0.75 (define @t34 () (_ tptp.var @t5)) % 0.41/0.75 (define @t35 () (@var "P" (-> tptp.term Bool))) % 0.41/0.75 (define @t36 () (_ @t35 @t5)) % 0.41/0.75 (define @t37 () (forall @t14 (=> @t34 @t36))) % 0.41/0.75 (define @t38 () (@list @t35)) % 0.41/0.75 (define @t39 () (= @t5 @t2)) % 0.41/0.75 (define @t40 () (@var "D" tptp.term)) % 0.41/0.75 (define @t41 () (_ tptp.ap @t2)) % 0.41/0.75 (define @t42 () (_ @t41 @t40)) % 0.41/0.75 (define @t43 () (@var "C" tptp.term)) % 0.41/0.75 (define @t44 () (_ @t8 @t43)) % 0.41/0.75 (define @t45 () (= @t44 @t42)) % 0.41/0.75 (define @t46 () (@list @t5 @t2 @t43 @t40)) % 0.41/0.75 (define @t47 () (forall @t46 (=> @t45 @t39))) % 0.41/0.75 (define @t48 () (= tptp.apinj1 @t47)) % 0.41/0.75 (define @t49 () (= @t43 @t40)) % 0.41/0.75 (define @t50 () (@list @t5 @t2)) % 0.41/0.75 (define @t51 () (forall @t14 @t36)) % 0.41/0.75 (define @t52 () (_ @t35 @t19)) % 0.41/0.75 (define @t53 () (_ @t35 @t2)) % 0.41/0.75 (define @t54 () (forall @t50 (=> @t36 (=> @t53 (_ @t35 @t9))))) % 0.41/0.75 (define @t55 () (@var "Q" (-> tptp.term Bool))) % 0.41/0.75 (define @t56 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t35) @t55)) % 0.41/0.75 (define @t57 () (@list @t55)) % 0.41/0.75 (define @t58 () (@list @t35 @t5 @t1)) % 0.41/0.75 (define @t59 () (_ tptp.push @t2)) % 0.41/0.75 (define @t60 () (@var "K" (-> tptp.term Bool))) % 0.41/0.75 (define @t61 () (@list @t35 @t55 @t5 @t1)) % 0.41/0.75 (define @t62 () (_ tptp.sub @t43)) % 0.41/0.75 (define @t63 () (@list @t43)) % 0.41/0.75 (define @t64 () (_ tptp.var @t2)) % 0.41/0.75 (define @t65 () (@list @t2)) % 0.41/0.75 (define @t66 () (forall @t65 (=> @t64 (_ @t35 @t4)))) % 0.41/0.75 (define @t67 () (_ @t3 @t10)) % 0.41/0.75 (define @t68 () (forall @t65 (=> @t64 (_ @t35 @t67)))) % 0.41/0.75 (define @t69 () (_ @t55 @t2)) % 0.41/0.75 (define @t70 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.41/0.75 (define @t71 () (_ @t6 (_ @t59 tptp.id))) % 0.41/0.75 (define @t72 () (forall @t14 (=> (forall @t65 (=> @t53 (_ @t35 @t71))) @t52))) % 0.41/0.75 (define @t73 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.41/0.75 (define @t74 () (=> tptp.induction2lem tptp.induction2)) % 0.41/0.75 (define @t75 () (_ tptp.hoasap tptp.id)) % 0.41/0.75 (define @t76 () (_ (_ @t75 @t5) tptp.id)) % 0.41/0.75 (define @t77 () (= (_ @t76 @t43) (_ (_ (_ @t75 @t2) tptp.id) @t40))) % 0.41/0.75 (define @t78 () (=> @t77 @t39)) % 0.41/0.75 (define @t79 () (forall @t46 @t78)) % 0.41/0.75 (define @t80 () (= tptp.hoasapinj1 @t79)) % 0.41/0.75 (define @t81 () (=> tptp.apinj1 tptp.hoasapinj1)) % 0.41/0.75 (define @t82 () (=> tptp.axvarid @t81)) % 0.41/0.75 (define @t83 () (= tptp.hoasapinj1_lthm @t82)) % 0.41/0.75 (define @t84 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.75 (define @t85 () (_ (_ @t84 @t1) @t5)) % 0.41/0.75 (define @t86 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.75 (define @t87 () (_ @t86 @t1)) % 0.41/0.75 (define @t88 () (_ @t87 @t5)) % 0.41/0.75 (define @t89 () (@list @t1 @t5)) % 0.41/0.75 (define @t90 () (_ tptp.hoaslam tptp.id)) % 0.41/0.75 (define @t91 () (_ @t90 (lambda @t89 @t88))) % 0.41/0.75 (define @t92 () (@list @t1 @t5 @t20)) % 0.41/0.75 (define @t93 () (_ (_ @t86 @t21) @t29)) % 0.41/0.75 (define @t94 () (_ (_ tptp.sub @t88) @t20)) % 0.41/0.75 (define @t95 () (forall @t92 (= @t94 @t93))) % 0.41/0.75 (define @t96 () (@list @t86)) % 0.41/0.75 (define @t97 () (_ @t76 @t2)) % 0.41/0.75 (define @t98 () (_ tptp.hoasvar tptp.id)) % 0.41/0.75 (define @t99 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.41/0.75 (define @t100 () (_ (_ tptp.hoasinduction_p_and_p_prime @t99) @t55)) % 0.41/0.75 (define @t101 () (@list @t99)) % 0.41/0.75 (define @t102 () (_ @t55 @t5)) % 0.41/0.75 (define @t103 () (_ @t99 tptp.id)) % 0.41/0.75 (define @t104 () (_ (_ @t103 @t5) tptp.id)) % 0.41/0.75 (define @t105 () (forall @t14 (=> (_ (_ @t98 @t5) tptp.id) @t104))) % 0.41/0.75 (define @t106 () (_ (_ (_ @t99 @t1) @t5) (_ (_ tptp.comp @t27) @t20))) % 0.41/0.75 (define @t107 () (_ (_ (_ @t99 (_ @t17 @t27)) (_ @t6 @t27)) @t20)) % 0.41/0.75 (define @t108 () (@list @t1 @t5 @t20 @t27)) % 0.41/0.75 (define @t109 () (forall @t108 (=> @t107 @t106))) % 0.41/0.75 (define @t110 () (forall @t108 (=> @t106 @t107))) % 0.41/0.75 (define @t111 () (@list @t99 @t55)) % 0.41/0.75 (define @t112 () (_ (_ @t103 @t2) tptp.id)) % 0.41/0.75 (define @t113 () (forall @t50 (=> @t104 (=> @t112 (_ (_ @t103 @t97) tptp.id))))) % 0.41/0.75 (define @t114 () (=> (forall @t14 (=> @t104 (_ (_ @t103 (_ (_ @t86 tptp.id) @t5)) tptp.id))) (_ (_ @t103 @t91) tptp.id))) % 0.41/0.75 (define @t115 () (forall @t96 (=> @t95 @t114))) % 0.41/0.75 (define @t116 () (=> @t115 (=> @t100 (forall @t14 (=> (forall @t65 (=> @t69 (_ @t55 @t71))) (_ @t55 @t19)))))) % 0.41/0.75 (define @t117 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1))))))))))))))))))))))))))))))))))) % 0.41/0.75 (define @t118 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2))))))))))))))))))))))))))))))))))) % 0.41/0.75 (define @t119 () (forall @t65 (=> @t112 (_ (_ @t103 @t71) tptp.id)))) % 0.41/0.75 (define @t120 () (forall @t14 (=> @t119 (_ (_ @t103 (_ tptp.lam (_ @t6 @t32))) tptp.id)))) % 0.41/0.75 (define @t121 () (=> @t115 (forall @t14 (=> @t119 (_ (_ @t103 @t19) tptp.id))))) % 0.41/0.75 (define @t122 () (_ (_ @t86 tptp.sh) tptp.one)) % 0.41/0.75 (define @t123 () (=> @t113 (=> @t115 (forall @t14 @t104)))) % 0.41/0.75 (define @t124 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.41/0.75 (define @t125 () (not tptp.hoasapinj1_lthm)) % 0.41/0.75 (define @t126 () (@var "X" tptp.term)) % 0.41/0.75 (define @t127 () (_ @t55 @t126)) % 0.41/0.75 (define @t128 () (@list @t126)) % 0.41/0.75 (define @t129 () (lambda (@list @t5 @t1 @t35 @t55) (forall @t128 (= @t127 (_ @t35 (_ (_ tptp.sub @t126) @t10)))))) % 0.41/0.75 (define @t130 () (_ tptp.ap @t29)) % 0.41/0.75 (define @t131 () (_ @t130 @t2)) % 0.41/0.75 (define @t132 () (lambda (@list @t1 @t5 @t20 @t2) @t131)) % 0.41/0.75 (define @t133 () (lambda (@list @t1 @t86) (_ tptp.lam @t122))) % 0.41/0.75 (define @t134 () (lambda @t92 (_ tptp.var @t29))) % 0.41/0.75 (define @t135 () (lambda @t111 (forall @t128 (= @t127 (_ (_ @t103 @t126) tptp.id))))) % 0.41/0.75 (define @t136 () (_ @t3 tptp.id)) % 0.41/0.75 (define @t137 () (tptp.sub @t2 tptp.id)) % 0.41/0.75 (define @t138 () (tptp.ap @t137 @t40)) % 0.41/0.75 (define @t139 () (_ tptp.ap @t136)) % 0.41/0.75 (define @t140 () (_ @t139 @t40)) % 0.41/0.75 (define @t141 () (tptp.sub @t5 tptp.id)) % 0.41/0.75 (define @t142 () (tptp.ap @t141 @t43)) % 0.41/0.75 (define @t143 () (_ tptp.ap @t13)) % 0.41/0.75 (define @t144 () (_ @t143 @t43)) % 0.41/0.75 (define @t145 () (= @t144 @t140)) % 0.41/0.75 (define @t146 () (not @t145)) % 0.41/0.75 (define @t147 () (or @t146 @t39)) % 0.41/0.75 (define @t148 () (@var "BOUND_VARIABLE_9440" tptp.term)) % 0.41/0.75 (define @t149 () (lambda (@list @t148) (_ @t139 @t148))) % 0.41/0.75 (define @t150 () (lambda (@list @t20 @t148) (_ (_ tptp.ap (_ @t3 @t20)) @t148))) % 0.41/0.75 (define @t151 () (lambda (@list @t5 @t20 @t2) @t131)) % 0.41/0.75 (define @t152 () (_ @t132 tptp.id)) % 0.41/0.75 (define @t153 () (lambda @t65 (_ @t143 @t2))) % 0.41/0.75 (define @t154 () (lambda (@list @t20 @t2) @t131)) % 0.41/0.75 (define @t155 () (= (_ (_ (_ @t152 @t5) tptp.id) @t43) (_ (_ (_ @t152 @t2) tptp.id) @t40))) % 0.41/0.75 (define @t156 () (=> @t155 @t39)) % 0.41/0.75 (define @t157 () (forall @t46 @t156)) % 0.41/0.75 (define @t158 () (tptp.ap @t2 @t40)) % 0.41/0.75 (define @t159 () (tptp.ap @t5 @t43)) % 0.41/0.75 (define @t160 () (not @t45)) % 0.41/0.75 (define @t161 () (or @t160 @t39)) % 0.41/0.75 (define @t162 () (= @t5 @t13)) % 0.41/0.75 (define @t163 () (forall @t46 (or (not (= @t142 @t138)) @t39))) % 0.41/0.75 (define @t164 () (@quantifiers_skolemize @t163 1)) % 0.41/0.75 (define @t165 () (@quantifiers_skolemize @t163 0)) % 0.41/0.75 (define @t166 () (= @t165 @t164)) % 0.41/0.75 (define @t167 () (@quantifiers_skolemize @t163 3)) % 0.41/0.75 (define @t168 () (tptp.sub @t164 tptp.id)) % 0.41/0.75 (define @t169 () (@quantifiers_skolemize @t163 2)) % 0.41/0.75 (define @t170 () (tptp.sub @t165 tptp.id)) % 0.41/0.75 (define @t171 () (= (tptp.ap @t170 @t169) (tptp.ap @t168 @t167))) % 0.41/0.75 (define @t172 () (not @t171)) % 0.41/0.75 (define @t173 () (or @t172 @t166)) % 0.41/0.75 (define @t174 () (not @t166)) % 0.41/0.75 (define @t175 () (@list true)) % 0.41/0.75 (define @t176 () (@list @t173)) % 0.41/0.75 (define @t177 () (= @t170 @t168)) % 0.41/0.75 (define @t178 () (or @t172 @t177)) % 0.41/0.75 (define @t179 () (not @t177)) % 0.41/0.75 (define @t180 () (= @t164 @t168)) % 0.41/0.75 (define @t181 () (not @t180)) % 0.41/0.75 (define @t182 () (= @t165 @t170)) % 0.41/0.75 (define @t183 () (not @t182)) % 0.41/0.75 (define @t184 () (and @t174 @t182 @t180)) % 0.41/0.75 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 0.41/0.75 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 0.41/0.75 (assume @p3 @t16) % 0.41/0.75 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t19) @t1) (_ tptp.lam (_ @t6 (_ @t18 (_ @t17 tptp.sh)))))))) % 0.41/0.75 (assume @p5 (= tptp.axclos @t23)) % 0.41/0.75 (assume @p6 (= tptp.axidl @t25)) % 0.41/0.75 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t26 @t10) @t1)))) % 0.41/0.75 (assume @p8 (= tptp.axassoc @t28)) % 0.41/0.75 (assume @p9 (= tptp.axmap (forall @t22 (= (_ (_ tptp.comp @t10) @t20) @t30)))) % 0.41/0.75 (assume @p10 (= tptp.axidr @t31)) % 0.41/0.75 (assume @p11 (= tptp.axvarshift (= @t32 tptp.id))) % 0.41/0.75 (assume @p12 (= tptp.axscons (forall @t24 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t26 @t1)) @t1)))) % 0.41/0.75 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 0.41/0.75 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t34 (_ tptp.var @t33))))) % 0.41/0.75 (assume @p15 (= tptp.ulamvarind (forall @t38 (=> (_ @t35 tptp.one) (=> (forall @t14 (=> @t34 (=> @t36 (_ @t35 @t33)))) @t37))))) % 0.41/0.75 (assume @p16 @t48) % 0.41/0.75 (assume @p17 (= tptp.apinj2 (forall @t46 (=> @t45 @t49)))) % 0.41/0.75 (assume @p18 (= tptp.laminj (forall @t50 (=> (= @t19 (_ tptp.lam @t2)) @t39)))) % 0.41/0.75 (assume @p19 (= tptp.shinj (forall @t50 (=> (= @t33 (_ @t3 tptp.sh)) @t39)))) % 0.41/0.75 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t43) (not (= @t19 (_ @t41 @t43)))))) % 0.41/0.75 (assume @p21 (= tptp.apnotvar (forall @t50 (not (_ tptp.var @t9))))) % 0.41/0.75 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t19))))) % 0.41/0.75 (assume @p23 (= tptp.induction (forall @t38 (=> @t37 (=> @t54 (=> (forall @t14 (=> @t36 @t52)) @t51)))))) % 0.41/0.75 (assume @p24 (= tptp.pushprop_lem0 (forall @t58 (exists @t57 @t56)))) % 0.41/0.75 (assume @p25 (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0))))))))))))))))))))))))) % 0.41/0.75 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.41/0.75 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t35 @t60 @t5 @t1 @t2) (=> @t36 (_ @t60 (_ @t6 (_ @t59 @t1))))))) % 0.41/0.75 (assume @p28 (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1))))))))))))))))))))))))) % 0.41/0.75 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.41/0.75 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t61 (=> @t36 (=> @t56 (_ @t55 tptp.one)))))) % 0.41/0.75 (assume @p31 (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2))))))))))))))))))))))))) % 0.41/0.75 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.41/0.75 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t61 (=> @t56 (=> @t66 (forall @t63 (=> (_ tptp.var @t43) (=> (_ @t55 @t43) (_ @t55 (_ @t62 tptp.sh)))))))))) % 0.41/0.75 (assume @p34 (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2))))))))))))))))))))))))) % 0.41/0.75 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.41/0.75 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t61 (=> @t56 (=> (forall @t65 (=> @t64 @t69)) @t68))))) % 0.41/0.75 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.41/0.75 (assume @p38 (= tptp.pushprop (forall @t58 (=> @t66 (=> @t36 @t68))))) % 0.41/0.75 (assume @p39 (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop))))))))))))))))))))))))) % 0.41/0.75 (assume @p40 (= tptp.pushprop_lthm_orig @t70)) % 0.41/0.75 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t70))) % 0.41/0.75 (assume @p42 (= tptp.induction2lem (forall @t38 (=> @t54 (=> @t72 (forall @t12 (=> @t66 (_ @t35 @t7)))))))) % 0.41/0.75 (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 @t73)))))))))))))))))))))))) % 0.41/0.75 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t73)))))))))) % 0.41/0.75 (assume @p45 (= tptp.induction2 (forall @t38 (=> @t37 (=> @t54 (=> @t72 @t51)))))) % 0.41/0.75 (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 @t74)))))))))))))))))))))))))) % 0.41/0.75 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t74))) % 0.41/0.75 (assume @p48 (= tptp.substmonoid (and @t28 @t25 @t31))) % 0.41/0.75 (assume @p49 (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid)))))))))))))))))))))))))))) % 0.41/0.75 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.41/0.75 (assume @p51 (= tptp.termmset (and @t23 @t15))) % 0.41/0.75 (assume @p52 (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.41/0.75 (assume @p54 @t80) % 0.41/0.75 (assume @p55 (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1)))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p56 @t83) % 0.41/0.75 (assume @p57 (= tptp.hoasapinj2 (forall @t46 (=> @t77 @t49)))) % 0.41/0.75 (assume @p58 (= tptp.hoasapinj2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 tptp.hoasapinj2))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.41/0.75 (assume @p60 (= tptp.hoaslaminj (forall @t96 (=> @t95 (forall (@list @t84) (=> (forall @t92 (= (_ (_ tptp.sub @t85) @t20) (_ (_ @t84 @t21) @t29))) (=> (= @t91 (_ @t90 (lambda @t89 @t85))) (forall @t89 (= @t88 @t85))))))))) % 0.41/0.75 (assume @p61 (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj)))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.41/0.75 (assume @p63 (= tptp.hoaslamnotap (forall @t96 (=> @t95 (forall @t50 (not (= (_ @t90 (lambda (@list @t1 @t43) (_ @t87 @t43))) @t97))))))) % 0.41/0.75 (assume @p64 (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.41/0.75 (assume @p66 (= tptp.hoaslamnotvar (forall @t96 (=> @t95 (not (_ (_ @t98 @t91) tptp.id)))))) % 0.41/0.75 (assume @p67 (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar)))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.41/0.75 (assume @p69 (= tptp.hoasapnotvar (forall @t50 (not (_ (_ @t98 @t97) tptp.id))))) % 0.41/0.75 (assume @p70 (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.41/0.75 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t101 (exists @t57 @t100)))) % 0.41/0.75 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.41/0.75 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t111 (=> @t110 (=> @t109 (=> @t105 (=> @t100 (forall @t14 (=> @t34 @t102))))))))) % 0.41/0.75 (assume @p75 (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t111 (=> @t110 (=> @t109 (=> @t113 (=> @t100 (forall @t50 (=> @t102 (=> @t69 (_ @t55 @t9))))))))))) % 0.41/0.75 (assume @p77 (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t65 (exists @t96 (forall @t12 (= @t88 @t67)))))) % 0.41/0.75 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.41/0.75 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t111 (=> @t110 (=> @t109 @t116))))) % 0.41/0.75 (assume @p81 (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2)))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.41/0.75 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t111 @t116))) % 0.41/0.75 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.41/0.75 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t101 (=> @t110 (=> @t109 (=> @t105 (forall @t14 (=> @t34 @t104)))))))) % 0.41/0.75 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t117)) % 0.41/0.75 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t117)) % 0.41/0.75 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t101 (=> @t110 (=> @t109 (=> @t113 (forall @t50 (=> @t104 (=> @t112 (_ (_ @t103 @t9) tptp.id)))))))))) % 0.41/0.75 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t118)) % 0.41/0.75 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t118)) % 0.41/0.75 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t101 (=> @t115 @t120)))) % 0.41/0.75 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.41/0.75 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t101 (=> (forall @t96 (=> (exists @t63 (forall @t92 (and (= @t94 (_ (_ tptp.sub (_ @t62 @t10)) @t20)) (= (_ @t62 @t30) @t93)))) @t114)) @t120)))) % 0.41/0.75 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t101 (=> @t110 (=> @t109 @t121))))) % 0.41/0.75 (assume @p95 (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3)))))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.41/0.75 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t101 @t121))) % 0.41/0.75 (assume @p98 (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a)))))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.41/0.75 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t65 (exists @t96 (= (_ @t3 @t32) @t122))))) % 0.41/0.75 (assume @p101 (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b)))))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.41/0.75 (assume @p103 (= tptp.hoasinduction (forall @t101 (=> @t110 (=> @t109 (=> @t105 @t123)))))) % 0.41/0.75 (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 @t124)))))))))))))))))))))))))))))))))))) % 0.41/0.75 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t124))) % 0.41/0.75 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.41/0.75 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t101 @t123))) % 0.41/0.75 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.41/0.75 (assume @p109 @t125) % 0.41/0.75 (assume @p110 true) % 0.41/0.75 (step @p111 (= tptp.pushprop_p_and_p_prime @t129) :rule refl :args (@t129)) % 0.41/0.75 (step @p112 (= tptp.hoasap @t132) :rule refl :args (@t132)) % 0.41/0.75 (step @p113 (= tptp.hoaslam @t133) :rule refl :args (@t133)) % 0.41/0.75 (step @p114 (= tptp.hoasvar @t134) :rule refl :args (@t134)) % 0.41/0.75 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t135) :rule refl :args (@t135)) % 0.41/0.75 (step @p116 :rule refl :args (@t39)) % 0.41/0.75 (step @p117 :rule refl :args ((tptp.ap @t136 @t40))) % 0.41/0.75 (step @p118 :rule refl :args (@t40)) % 0.41/0.75 (step @p119 :rule refl :args (@t137)) % 0.41/0.75 (step @p120 :rule cong :premises (@p119 @p118) :args (@t138)) % 0.41/0.75 (step @p121 :rule trans :premises (@p120 @p117)) % 0.41/0.75 (step @p122 :rule refl :args (tptp.ap)) % 0.41/0.75 (step @p123 :rule ho_cong :premises (@p122 @p119)) % 0.41/0.75 (step @p124 :rule ho_cong :premises (@p123 @p118)) % 0.41/0.75 (step @p125 :rule cong :premises (@p124 @p121) :args ((= (_ (_ tptp.ap @t137) @t40) @t138))) % 0.41/0.75 (step @p126 :rule symm :premises (@p125)) % 0.41/0.75 (step @p127 :rule refl :args (@t140)) % 0.41/0.75 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 0.41/0.75 (step @p129 :rule refl :args (@t136)) % 0.41/0.75 (step @p130 :rule cong :premises (@p129 @p119) :args ((= @t136 @t137))) % 0.41/0.75 (step @p131 :rule symm :premises (@p130)) % 0.41/0.75 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 0.41/0.75 (step @p133 :rule ho_cong :premises (@p122 @p132)) % 0.41/0.75 (step @p134 :rule ho_cong :premises (@p133 @p118)) % 0.41/0.75 (step @p135 :rule trans :premises (@p134 @p128)) % 0.41/0.75 (step @p136 :rule refl :args ((tptp.ap @t13 @t43))) % 0.41/0.75 (step @p137 :rule refl :args (@t43)) % 0.41/0.75 (step @p138 :rule refl :args (@t141)) % 0.41/0.75 (step @p139 :rule cong :premises (@p138 @p137) :args (@t142)) % 0.41/0.75 (step @p140 :rule trans :premises (@p139 @p136)) % 0.41/0.75 (step @p141 :rule ho_cong :premises (@p122 @p138)) % 0.41/0.75 (step @p142 :rule ho_cong :premises (@p141 @p137)) % 0.41/0.75 (step @p143 :rule cong :premises (@p142 @p140) :args ((= (_ (_ tptp.ap @t141) @t43) @t142))) % 0.41/0.75 (step @p144 :rule symm :premises (@p143)) % 0.41/0.75 (step @p145 :rule refl :args (@t144)) % 0.41/0.75 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 0.41/0.75 (step @p147 :rule refl :args (@t13)) % 0.41/0.75 (step @p148 :rule cong :premises (@p147 @p138) :args ((= @t13 @t141))) % 0.41/0.75 (step @p149 :rule symm :premises (@p148)) % 0.41/0.75 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 0.41/0.75 (step @p151 :rule ho_cong :premises (@p122 @p150)) % 0.41/0.75 (step @p152 :rule ho_cong :premises (@p151 @p137)) % 0.41/0.75 (step @p153 :rule trans :premises (@p152 @p146)) % 0.41/0.75 (step @p154 :rule cong :premises (@p153 @p135) :args (@t145)) % 0.41/0.75 (step @p155 :rule cong :premises (@p154) :args (@t146)) % 0.41/0.75 (step @p156 :rule nary_cong :premises (@p155 @p116) :args (@t147)) % 0.41/0.75 (step @p157 :rule cong :premises (@p156) :args ((forall @t46 @t147))) % 0.41/0.75 (step @p158 :rule bool-impl-elim :args (@t145 @t39)) % 0.41/0.75 (step @p159 :rule cong :premises (@p158) :args ((forall @t46 (=> @t145 @t39)))) % 0.41/0.75 (step @p160 :rule trans :premises (@p159 @p157)) % 0.41/0.75 (step @p161 :rule refl :args (@t39)) % 0.41/0.75 (step @p162 :rule beta-reduce :args ((= (_ @t149 @t40) @t140))) % 0.41/0.75 (step @p163 :rule refl :args (@t40)) % 0.41/0.75 (step @p164 :rule beta-reduce :args ((= (_ @t150 tptp.id) @t149))) % 0.41/0.75 (step @p165 :rule refl :args (tptp.id)) % 0.41/0.75 (step @p166 :rule beta-reduce :args ((= (_ (lambda (@list @t5 @t20 @t148) (_ @t130 @t148)) @t2) @t150))) % 0.41/0.75 (step @p167 :rule refl :args (@t2)) % 0.41/0.75 (step @p168 :rule alpha_equiv :args (@t151 (@list @t2) (@list @t148))) % 0.41/0.75 (step @p169 :rule ho_cong :premises (@p168 @p167)) % 0.41/0.75 (step @p170 :rule trans :premises (@p169 @p166)) % 0.41/0.75 (step @p171 :rule refl :args (@t2)) % 0.41/0.75 (step @p172 :rule beta-reduce :args ((= @t152 @t151))) % 0.41/0.75 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 0.41/0.75 (step @p174 :rule trans :premises (@p173 @p170)) % 0.41/0.75 (step @p175 :rule ho_cong :premises (@p174 @p165)) % 0.41/0.75 (step @p176 :rule trans :premises (@p175 @p164)) % 0.41/0.75 (step @p177 :rule ho_cong :premises (@p176 @p163)) % 0.41/0.75 (step @p178 :rule trans :premises (@p177 @p162)) % 0.41/0.75 (step @p179 :rule beta-reduce :args ((= (_ @t153 @t43) @t144))) % 0.41/0.75 (step @p180 :rule refl :args (@t43)) % 0.41/0.75 (step @p181 :rule beta-reduce :args ((= (_ @t154 tptp.id) @t153))) % 0.41/0.75 (step @p182 :rule beta-reduce :args ((= (_ @t151 @t5) @t154))) % 0.41/0.75 (step @p183 :rule refl :args (@t5)) % 0.41/0.75 (step @p184 :rule ho_cong :premises (@p172 @p183)) % 0.41/0.75 (step @p185 :rule trans :premises (@p184 @p182)) % 0.41/0.75 (step @p186 :rule ho_cong :premises (@p185 @p165)) % 0.41/0.75 (step @p187 :rule trans :premises (@p186 @p181)) % 0.41/0.75 (step @p188 :rule ho_cong :premises (@p187 @p180)) % 0.41/0.75 (step @p189 :rule trans :premises (@p188 @p179)) % 0.41/0.75 (step @p190 :rule cong :premises (@p189 @p178) :args (@t155)) % 0.41/0.75 (step @p191 :rule cong :premises (@p190 @p161) :args (@t156)) % 0.41/0.75 (step @p192 :rule cong :premises (@p191) :args (@t157)) % 0.41/0.75 (step @p193 :rule trans :premises (@p192 @p160)) % 0.41/0.75 (step @p194 :rule refl :args (tptp.hoasapinj1)) % 0.41/0.75 (step @p195 :rule cong :premises (@p194 @p193) :args ((= tptp.hoasapinj1 @t157))) % 0.41/0.75 (step @p196 :rule ho_cong :premises (@p112 @p165)) % 0.41/0.75 (step @p197 :rule ho_cong :premises (@p196 @p171)) % 0.41/0.75 (step @p198 :rule ho_cong :premises (@p197 @p165)) % 0.41/0.75 (step @p199 :rule ho_cong :premises (@p198 @p163)) % 0.41/0.75 (step @p200 :rule ho_cong :premises (@p196 @p183)) % 0.41/0.75 (step @p201 :rule ho_cong :premises (@p200 @p165)) % 0.41/0.75 (step @p202 :rule ho_cong :premises (@p201 @p180)) % 0.41/0.75 (step @p203 :rule cong :premises (@p202 @p199) :args (@t77)) % 0.41/0.75 (step @p204 :rule cong :premises (@p203 @p161) :args (@t78)) % 0.41/0.75 (step @p205 :rule cong :premises (@p204) :args (@t79)) % 0.41/0.75 (step @p206 :rule cong :premises (@p194 @p205) :args (@t80)) % 0.41/0.75 (step @p207 :rule trans :premises (@p206 @p195)) % 0.41/0.75 (step @p208 :rule eq_resolve :premises (@p54 @p207)) % 0.41/0.75 (step @p209 :rule refl :args (@t158)) % 0.41/0.75 (step @p210 :rule refl :args (@t42)) % 0.41/0.75 (step @p211 :rule cong :premises (@p210 @p209) :args ((= @t42 @t158))) % 0.41/0.75 (step @p212 :rule symm :premises (@p211)) % 0.41/0.75 (step @p213 :rule eq_resolve :premises (@p210 @p212)) % 0.41/0.75 (step @p214 :rule refl :args (@t159)) % 0.41/0.75 (step @p215 :rule refl :args (@t44)) % 0.41/0.75 (step @p216 :rule cong :premises (@p215 @p214) :args ((= @t44 @t159))) % 0.41/0.75 (step @p217 :rule symm :premises (@p216)) % 0.41/0.75 (step @p218 :rule eq_resolve :premises (@p215 @p217)) % 0.41/0.75 (step @p219 :rule cong :premises (@p218 @p213) :args (@t45)) % 0.41/0.75 (step @p220 :rule cong :premises (@p219) :args (@t160)) % 0.41/0.75 (step @p221 :rule nary_cong :premises (@p220 @p116) :args (@t161)) % 0.41/0.75 (step @p222 :rule cong :premises (@p221) :args ((forall @t46 @t161))) % 0.41/0.75 (step @p223 :rule bool-impl-elim :args (@t45 @t39)) % 0.41/0.75 (step @p224 :rule cong :premises (@p223) :args (@t47)) % 0.41/0.75 (step @p225 :rule trans :premises (@p224 @p222)) % 0.41/0.75 (step @p226 :rule refl :args (tptp.apinj1)) % 0.41/0.75 (step @p227 :rule cong :premises (@p226 @p225) :args (@t48)) % 0.41/0.75 (step @p228 :rule eq_resolve :premises (@p16 @p227)) % 0.41/0.75 (step @p229 :rule cong :premises (@p228 @p208) :args (@t81)) % 0.41/0.75 (step @p230 :rule refl :args (@t5)) % 0.41/0.75 (step @p231 :rule cong :premises (@p230 @p150) :args (@t162)) % 0.41/0.75 (step @p232 :rule cong :premises (@p231) :args ((forall @t14 @t162))) % 0.41/0.75 (step @p233 :rule eq-symm :args (@t13 @t5)) % 0.41/0.75 (step @p234 :rule cong :premises (@p233) :args (@t15)) % 0.41/0.75 (step @p235 :rule trans :premises (@p234 @p232)) % 0.41/0.75 (step @p236 :rule refl :args (tptp.axvarid)) % 0.41/0.75 (step @p237 :rule cong :premises (@p236 @p235) :args (@t16)) % 0.41/0.75 (step @p238 :rule eq_resolve :premises (@p3 @p237)) % 0.41/0.75 (step @p239 :rule cong :premises (@p238 @p229) :args (@t82)) % 0.41/0.75 (step @p240 :rule refl :args (tptp.hoasapinj1_lthm)) % 0.41/0.75 (step @p241 :rule cong :premises (@p240 @p239) :args (@t83)) % 0.41/0.75 (step @p242 :rule eq_resolve :premises (@p56 @p241)) % 0.41/0.75 (step @p243 :rule cong :premises (@p242) :args (@t125)) % 0.41/0.75 (step @p244 :rule eq_resolve :premises (@p109 @p243)) % 0.41/0.75 (step @p245 :rule not_implies_elim2 :premises (@p244)) % 0.41/0.75 (step @p246 :rule not_implies_elim2 :premises (@p245)) % 0.41/0.75 (step @p247 :rule skolemize :premises (@p246)) % 0.41/0.75 (step @p248 :rule cnf_or_neg :args (@t173 1)) % 0.41/0.75 (step @p249 :rule chain_m_resolution :premises (@p248 @p247) :args (@t174 @t175 @t176)) % 0.41/0.75 (step @p250 :rule not_implies_elim1 :premises (@p244)) % 0.41/0.75 (step @p251 :rule instantiate :premises (@p250) :args ((@list @t165))) % 0.41/0.75 (step @p252 :rule instantiate :premises (@p250) :args ((@list @t164))) % 0.41/0.75 (step @p253 :rule not_implies_elim1 :premises (@p245)) % 0.41/0.75 (step @p254 :rule instantiate :premises (@p253) :args ((@list @t170 @t168 @t169 @t167))) % 0.41/0.75 (step @p255 :rule bool-double-not-elim :args (@t171)) % 0.41/0.75 (step @p256 :rule refl :args (@t173)) % 0.41/0.75 (step @p257 :rule nary_cong :premises (@p256 @p255) :args ((or @t173 (not @t172)))) % 0.41/0.75 (step @p258 :rule cnf_or_neg :args (@t173 0)) % 0.41/0.75 (step @p259 :rule eq_resolve :premises (@p258 @p257)) % 0.41/0.75 (step @p260 :rule reordering :premises (@p259) :args ((or @t171 @t173))) % 0.41/0.75 (step @p261 :rule chain_m_resolution :premises (@p260 @p247) :args (@t171 @t175 @t176)) % 0.41/0.75 (step @p262 :rule cnf_or_pos :args (@t178)) % 0.41/0.75 (step @p263 :rule reordering :premises (@p262) :args ((or @t172 @t177 (not @t178)))) % 0.41/0.75 (step @p264 :rule chain_m_resolution :premises (@p263 @p261 @p254) :args (@t177 (@list false false) (@list @t171 @t178))) % 0.41/0.75 (step @p265 :rule refl :args (@t179)) % 0.41/0.75 (step @p266 :rule refl :args (@t181)) % 0.41/0.75 (step @p267 :rule refl :args (@t183)) % 0.41/0.75 (step @p268 :rule bool-double-not-elim :args (@t166)) % 0.41/0.75 (step @p269 :rule nary_cong :premises (@p268 @p267 @p266 @p265) :args ((or (not @t174) @t183 @t181 @t179))) % 0.41/0.75 (assume-push @p288 @t174) % 0.41/0.75 (assume-push @p289 @t182) % 0.41/0.75 (assume-push @p290 @t180) % 0.41/0.75 (step @p273 :rule false_intro :premises (@p249)) % 0.41/0.75 (step @p274 :rule symm :premises (@p252)) % 0.41/0.75 (step @p275 :rule symm :premises (@p251)) % 0.41/0.75 (step @p276 :rule cong :premises (@p275 @p274) :args (@t177)) % 0.41/0.75 (step @p277 :rule trans :premises (@p276 @p273)) % 0.41/0.75 (step @p278 :rule false_elim :premises (@p277)) % 0.41/0.75 (step-pop @p291 :rule scope :premises (@p278)) % 0.41/0.75 (step-pop @p292 :rule scope :premises (@p291)) % 0.41/0.75 (step-pop @p293 :rule scope :premises (@p292)) % 0.41/0.75 (step @p279 :rule process_scope :premises (@p293) :args (@t179)) % 0.41/0.75 (step @p283 :rule implies_elim :premises (@p279)) % 0.41/0.75 (step @p284 :rule cnf_and_neg :args (@t184)) % 0.41/0.75 (step @p285 :rule resolution :premises (@p284 @p283) :args (true @t184)) % 0.41/0.75 (step @p286 :rule eq_resolve :premises (@p285 @p269)) % 0.41/0.75 (step @p287 false :rule chain_m_resolution :premises (@p286 @p264 @p252 @p251 @p249) :args (false (@list false false false true) (@list @t177 @t180 @t182 @t166))) % 0.41/0.75 ) % 0.41/0.75 % SZS output end Proof % 0.41/0.75 % cvc5 exiting %------------------------------------------------------------------------------