%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG253^2 : 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 150.98s 151.30s % Output : Proof 150.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ALG253^2 : 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 % 0.17/0.35 % Computer : n025.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 01:55:16 EDT 2026 % 0.17/0.35 % CPUTime : % 0.41/0.58 %----Proving TH0 % 150.98/151.30 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.98/151.30 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 150.98/151.30 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 150.98/151.30 --- Run --ho-elim --full-saturate-quant at 18s... % 150.98/151.30 % SZS status Theorem % 150.98/151.30 % SZS output start Proof % 150.98/151.30 ( % 150.98/151.30 (declare-sort tptp.subst 0) % 150.98/151.30 (declare-sort tptp.term 0) % 150.98/151.30 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 150.98/151.30 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 150.98/151.30 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 150.98/151.30 (declare-const tptp.one tptp.term) % 150.98/151.30 (declare-const tptp.sh tptp.subst) % 150.98/151.30 (declare-const tptp.lam (-> tptp.term tptp.term)) % 150.98/151.30 (declare-const tptp.var (-> tptp.term Bool)) % 150.98/151.30 (declare-const tptp.id tptp.subst) % 150.98/151.30 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lthm_3 Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3b Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3a Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3 Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3aaa Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3aa Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem2 Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem1 Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3v2a Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3v2 Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem2v2 Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem1v2 Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasinduction_lem0 Bool) % 150.98/151.30 (declare-const tptp.hoasapnotvar_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasapnotvar_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasapnotvar Bool) % 150.98/151.30 (declare-const tptp.hoaslamnotvar_lthm Bool) % 150.98/151.30 (declare-const tptp.hoaslamnotvar_gthm Bool) % 150.98/151.30 (declare-const tptp.hoaslamnotvar Bool) % 150.98/151.30 (declare-const tptp.hoaslamnotap_lthm Bool) % 150.98/151.30 (declare-const tptp.hoaslamnotap_gthm Bool) % 150.98/151.30 (declare-const tptp.hoaslamnotap Bool) % 150.98/151.30 (declare-const tptp.hoaslaminj_lthm Bool) % 150.98/151.30 (declare-const tptp.hoaslaminj_gthm Bool) % 150.98/151.30 (declare-const tptp.hoaslaminj Bool) % 150.98/151.30 (declare-const tptp.hoasapinj2_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasapinj2_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasapinj2 Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem0_lthm Bool) % 150.98/151.30 (declare-const tptp.axassoc Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem0_gthm Bool) % 150.98/151.30 (declare-const tptp.axvarcons Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem0 Bool) % 150.98/151.30 (declare-const tptp.apinj1 Bool) % 150.98/151.30 (declare-const tptp.induction Bool) % 150.98/151.30 (declare-const tptp.apnotvar Bool) % 150.98/151.30 (declare-const tptp.laminj Bool) % 150.98/151.30 (declare-const tptp.axvarshift Bool) % 150.98/151.30 (declare-const tptp.ulamvarind Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 150.98/151.30 (declare-const tptp.ulamvarsh Bool) % 150.98/151.30 (declare-const tptp.ulamvar1 Bool) % 150.98/151.30 (declare-const tptp.axabs Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem1 Bool) % 150.98/151.30 (declare-const tptp.shinj Bool) % 150.98/151.30 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 150.98/151.30 (declare-const tptp.apinj2 Bool) % 150.98/151.30 (declare-const tptp.axvarid Bool) % 150.98/151.30 (declare-const tptp.axidl Bool) % 150.98/151.30 (declare-const tptp.axclos Bool) % 150.98/151.30 (declare-const tptp.termmset Bool) % 150.98/151.30 (declare-const tptp.axshiftcons Bool) % 150.98/151.30 (declare-const tptp.lamnotap Bool) % 150.98/151.30 (declare-const tptp.lamnotvar Bool) % 150.98/151.30 (declare-const tptp.axapp Bool) % 150.98/151.30 (declare-const tptp.axscons Bool) % 150.98/151.30 (declare-const tptp.axmap Bool) % 150.98/151.30 (declare-const tptp.axidr Bool) % 150.98/151.30 (declare-const tptp.induction2lem Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem1_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasapinj1_lthm Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem1_lthm Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem1v2 Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 150.98/151.30 (declare-const tptp.induction2 Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem2v2 Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem3v2 Bool) % 150.98/151.30 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 150.98/151.30 (declare-const tptp.pushprop Bool) % 150.98/151.30 (declare-const tptp.pushprop_gthm Bool) % 150.98/151.30 (declare-const tptp.hoasapinj1 Bool) % 150.98/151.30 (declare-const tptp.pushprop_lthm_orig Bool) % 150.98/151.30 (declare-const tptp.pushprop_lthm Bool) % 150.98/151.30 (declare-const tptp.induction2lem_gthm Bool) % 150.98/151.30 (declare-const tptp.induction2lem_lthm Bool) % 150.98/151.30 (declare-const tptp.induction2_gthm Bool) % 150.98/151.30 (declare-const tptp.induction2_lthm Bool) % 150.98/151.30 (declare-const tptp.substmonoid Bool) % 150.98/151.30 (declare-const tptp.substmonoid_gthm Bool) % 150.98/151.30 (declare-const tptp.termmset_gthm Bool) % 150.98/151.30 (declare-const tptp.substmonoid_lthm Bool) % 150.98/151.30 (declare-const tptp.termmset_lthm Bool) % 150.98/151.30 (declare-const tptp.hoasapinj1_gthm Bool) % 150.98/151.30 (define tptp.pushprop_p_and_p_prime () (let ((_let_1 (@var "M" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (let ((_let_3 (@var "X" tptp.term))) (let ((_let_4 (@var "P" (-> tptp.term Bool)))) (let ((_let_5 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_1 _let_4 _let_5) (forall (@list _let_3) (= (_ _let_5 _let_3) (_ _let_4 (_ (_ tptp.sub _let_3) (_ (_ tptp.push _let_2) _let_1)))))))))))) % 150.98/151.30 (define tptp.hoasap () (let ((_let_1 (@var "B" tptp.term))) (let ((_let_2 (@var "N" tptp.subst))) (let ((_let_3 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_3 _let_2 _let_1) (_ (_ tptp.ap (_ (_ tptp.sub _let_3) _let_2)) _let_1)))))) % 150.98/151.30 (define tptp.hoaslam () (let ((_let_1 (@var "F" (-> tptp.subst tptp.term tptp.term)))) (lambda (@list (@var "M" tptp.subst) _let_1) (_ tptp.lam (_ (_ _let_1 tptp.sh) tptp.one))))) % 150.98/151.30 (define tptp.hoasvar () (let ((_let_1 (@var "N" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_2 _let_1) (_ tptp.var (_ (_ tptp.sub _let_2) _let_1)))))) % 150.98/151.30 (define tptp.hoasinduction_p_and_p_prime () (let ((_let_1 (@var "X" tptp.term))) (let ((_let_2 (@var "P" (-> tptp.subst tptp.term tptp.subst Bool)))) (let ((_let_3 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (= (_ _let_3 _let_1) (_ (_ (_ _let_2 tptp.id) _let_1) tptp.id)))))))) % 150.98/151.30 (define @t1 () (@var "M" tptp.subst)) % 150.98/151.30 (define @t2 () (@var "B" tptp.term)) % 150.98/151.30 (define @t3 () (_ tptp.sub @t2)) % 150.98/151.30 (define @t4 () (_ @t3 @t1)) % 150.98/151.30 (define @t5 () (@var "A" tptp.term)) % 150.98/151.30 (define @t6 () (_ tptp.sub @t5)) % 150.98/151.30 (define @t7 () (_ @t6 @t1)) % 150.98/151.30 (define @t8 () (_ tptp.ap @t5)) % 150.98/151.30 (define @t9 () (_ @t8 @t2)) % 150.98/151.30 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 150.98/151.30 (define @t11 () (_ tptp.sub tptp.one)) % 150.98/151.30 (define @t12 () (@list @t5 @t1)) % 150.98/151.30 (define @t13 () (_ @t6 tptp.id)) % 150.98/151.30 (define @t14 () (@list @t5)) % 150.98/151.30 (define @t15 () (forall @t14 (= @t13 @t5))) % 150.98/151.30 (define @t16 () (= tptp.axvarid @t15)) % 150.98/151.30 (define @t17 () (_ tptp.comp @t1)) % 150.98/151.30 (define @t18 () (_ tptp.push tptp.one)) % 150.98/151.30 (define @t19 () (_ tptp.lam @t5)) % 150.98/151.30 (define @t20 () (@var "N" tptp.subst)) % 150.98/151.30 (define @t21 () (_ @t17 @t20)) % 150.98/151.30 (define @t22 () (@list @t5 @t1 @t20)) % 150.98/151.30 (define @t23 () (forall @t22 (= (_ (_ tptp.sub @t7) @t20) (_ @t6 @t21)))) % 150.98/151.30 (define @t24 () (@list @t1)) % 150.98/151.30 (define @t25 () (forall @t24 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 150.98/151.30 (define @t26 () (_ tptp.comp tptp.sh)) % 150.98/151.30 (define @t27 () (@var "K" tptp.subst)) % 150.98/151.30 (define @t28 () (forall (@list @t1 @t20 @t27) (= (_ (_ tptp.comp @t21) @t27) (_ @t17 (_ (_ tptp.comp @t20) @t27))))) % 150.98/151.30 (define @t29 () (_ @t6 @t20)) % 150.98/151.30 (define @t30 () (_ (_ tptp.push @t29) @t21)) % 150.98/151.30 (define @t31 () (forall @t24 (= (_ @t17 tptp.id) @t1))) % 150.98/151.30 (define @t32 () (_ @t18 tptp.sh)) % 150.98/151.30 (define @t33 () (_ @t6 tptp.sh)) % 150.98/151.30 (define @t34 () (_ tptp.var @t5)) % 150.98/151.30 (define @t35 () (@var "P" (-> tptp.term Bool))) % 150.98/151.30 (define @t36 () (_ @t35 @t5)) % 150.98/151.30 (define @t37 () (forall @t14 (=> @t34 @t36))) % 150.98/151.30 (define @t38 () (@list @t35)) % 150.98/151.30 (define @t39 () (= @t5 @t2)) % 150.98/151.30 (define @t40 () (@var "D" tptp.term)) % 150.98/151.30 (define @t41 () (_ tptp.ap @t2)) % 150.98/151.30 (define @t42 () (@var "C" tptp.term)) % 150.98/151.30 (define @t43 () (= (_ @t8 @t42) (_ @t41 @t40))) % 150.98/151.30 (define @t44 () (@list @t5 @t2 @t42 @t40)) % 150.98/151.30 (define @t45 () (= @t42 @t40)) % 150.98/151.30 (define @t46 () (@list @t5 @t2)) % 150.98/151.30 (define @t47 () (forall @t14 @t36)) % 150.98/151.30 (define @t48 () (_ @t35 @t19)) % 150.98/151.30 (define @t49 () (_ @t35 @t9)) % 150.98/151.30 (define @t50 () (_ @t35 @t2)) % 150.98/151.30 (define @t51 () (=> @t50 @t49)) % 150.98/151.30 (define @t52 () (forall @t46 (=> @t36 @t51))) % 150.98/151.30 (define @t53 () (@var "Q" (-> tptp.term Bool))) % 150.98/151.30 (define @t54 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t35) @t53)) % 150.98/151.30 (define @t55 () (@list @t53)) % 150.98/151.30 (define @t56 () (@list @t35 @t5 @t1)) % 150.98/151.30 (define @t57 () (_ tptp.push @t2)) % 150.98/151.30 (define @t58 () (@var "K" (-> tptp.term Bool))) % 150.98/151.30 (define @t59 () (@list @t35 @t53 @t5 @t1)) % 150.98/151.30 (define @t60 () (_ tptp.sub @t42)) % 150.98/151.30 (define @t61 () (@list @t42)) % 150.98/151.30 (define @t62 () (_ @t35 @t4)) % 150.98/151.30 (define @t63 () (_ tptp.var @t2)) % 150.98/151.30 (define @t64 () (@list @t2)) % 150.98/151.30 (define @t65 () (forall @t64 (=> @t63 @t62))) % 150.98/151.30 (define @t66 () (_ @t3 @t10)) % 150.98/151.30 (define @t67 () (forall @t64 (=> @t63 (_ @t35 @t66)))) % 150.98/151.30 (define @t68 () (_ @t53 @t2)) % 150.98/151.30 (define @t69 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 150.98/151.30 (define @t70 () (_ @t35 @t7)) % 150.98/151.30 (define @t71 () (=> @t65 @t70)) % 150.98/151.30 (define @t72 () (forall @t12 @t71)) % 150.98/151.30 (define @t73 () (_ @t57 tptp.id)) % 150.98/151.30 (define @t74 () (_ @t6 @t73)) % 150.98/151.30 (define @t75 () (_ @t35 @t74)) % 150.98/151.30 (define @t76 () (forall @t64 (=> @t50 @t75))) % 150.98/151.30 (define @t77 () (=> @t76 @t48)) % 150.98/151.30 (define @t78 () (forall @t14 @t77)) % 150.98/151.30 (define @t79 () (=> @t78 @t72)) % 150.98/151.30 (define @t80 () (=> @t52 @t79)) % 150.98/151.30 (define @t81 () (forall @t38 @t80)) % 150.98/151.30 (define @t82 () (= tptp.induction2lem @t81)) % 150.98/151.30 (define @t83 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 150.98/151.30 (define @t84 () (=> @t78 @t47)) % 150.98/151.30 (define @t85 () (=> @t52 @t84)) % 150.98/151.30 (define @t86 () (=> @t37 @t85)) % 150.98/151.30 (define @t87 () (forall @t38 @t86)) % 150.98/151.30 (define @t88 () (= tptp.induction2 @t87)) % 150.98/151.30 (define @t89 () (=> tptp.induction2lem tptp.induction2)) % 150.98/151.30 (define @t90 () (=> tptp.axvarid @t89)) % 150.98/151.30 (define @t91 () (= tptp.induction2_lthm @t90)) % 150.98/151.30 (define @t92 () (_ tptp.hoasap tptp.id)) % 150.98/151.30 (define @t93 () (_ (_ @t92 @t5) tptp.id)) % 150.98/151.30 (define @t94 () (= (_ @t93 @t42) (_ (_ (_ @t92 @t2) tptp.id) @t40))) % 150.98/151.30 (define @t95 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 150.98/151.30 (define @t96 () (_ (_ @t95 @t1) @t5)) % 150.98/151.30 (define @t97 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 150.98/151.30 (define @t98 () (_ @t97 @t1)) % 150.98/151.30 (define @t99 () (_ @t98 @t5)) % 150.98/151.30 (define @t100 () (@list @t1 @t5)) % 150.98/151.30 (define @t101 () (_ tptp.hoaslam tptp.id)) % 150.98/151.30 (define @t102 () (_ @t101 (lambda @t100 @t99))) % 150.98/151.30 (define @t103 () (@list @t1 @t5 @t20)) % 150.98/151.30 (define @t104 () (_ (_ @t97 @t21) @t29)) % 150.98/151.30 (define @t105 () (_ (_ tptp.sub @t99) @t20)) % 150.98/151.30 (define @t106 () (forall @t103 (= @t105 @t104))) % 150.98/151.30 (define @t107 () (@list @t97)) % 150.98/151.30 (define @t108 () (_ @t93 @t2)) % 150.98/151.30 (define @t109 () (_ tptp.hoasvar tptp.id)) % 150.98/151.30 (define @t110 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 150.98/151.30 (define @t111 () (_ (_ tptp.hoasinduction_p_and_p_prime @t110) @t53)) % 150.98/151.30 (define @t112 () (@list @t110)) % 150.98/151.30 (define @t113 () (_ @t53 @t5)) % 150.98/151.30 (define @t114 () (_ @t110 tptp.id)) % 150.98/151.30 (define @t115 () (_ (_ @t114 @t5) tptp.id)) % 150.98/151.30 (define @t116 () (forall @t14 (=> (_ (_ @t109 @t5) tptp.id) @t115))) % 150.98/151.30 (define @t117 () (_ (_ (_ @t110 @t1) @t5) (_ (_ tptp.comp @t27) @t20))) % 150.98/151.30 (define @t118 () (_ (_ (_ @t110 (_ @t17 @t27)) (_ @t6 @t27)) @t20)) % 150.98/151.30 (define @t119 () (@list @t1 @t5 @t20 @t27)) % 150.98/151.30 (define @t120 () (forall @t119 (=> @t118 @t117))) % 150.98/151.30 (define @t121 () (forall @t119 (=> @t117 @t118))) % 150.98/151.30 (define @t122 () (@list @t110 @t53)) % 150.98/151.30 (define @t123 () (_ (_ @t114 @t2) tptp.id)) % 150.98/151.30 (define @t124 () (forall @t46 (=> @t115 (=> @t123 (_ (_ @t114 @t108) tptp.id))))) % 150.98/151.30 (define @t125 () (=> (forall @t14 (=> @t115 (_ (_ @t114 (_ (_ @t97 tptp.id) @t5)) tptp.id))) (_ (_ @t114 @t102) tptp.id))) % 150.98/151.30 (define @t126 () (forall @t107 (=> @t106 @t125))) % 150.98/151.30 (define @t127 () (=> @t126 (=> @t111 (forall @t14 (=> (forall @t64 (=> @t68 (_ @t53 @t74))) (_ @t53 @t19)))))) % 150.98/151.30 (define @t128 () (=> 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))))))))))))))))))))))))))))))))))) % 150.98/151.30 (define @t129 () (=> 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))))))))))))))))))))))))))))))))))) % 150.98/151.30 (define @t130 () (forall @t64 (=> @t123 (_ (_ @t114 @t74) tptp.id)))) % 150.98/151.30 (define @t131 () (forall @t14 (=> @t130 (_ (_ @t114 (_ tptp.lam (_ @t6 @t32))) tptp.id)))) % 150.98/151.30 (define @t132 () (=> @t126 (forall @t14 (=> @t130 (_ (_ @t114 @t19) tptp.id))))) % 150.98/151.30 (define @t133 () (_ (_ @t97 tptp.sh) tptp.one)) % 150.98/151.30 (define @t134 () (=> @t124 (=> @t126 (forall @t14 @t115)))) % 150.98/151.30 (define @t135 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 150.98/151.30 (define @t136 () (not tptp.induction2_lthm)) % 150.98/151.30 (define @t137 () (@var "X" tptp.term)) % 150.98/151.30 (define @t138 () (_ @t53 @t137)) % 150.98/151.30 (define @t139 () (@list @t137)) % 150.98/151.30 (define @t140 () (lambda (@list @t5 @t1 @t35 @t53) (forall @t139 (= @t138 (_ @t35 (_ (_ tptp.sub @t137) @t10)))))) % 150.98/151.30 (define @t141 () (lambda (@list @t1 @t5 @t20 @t2) (_ (_ tptp.ap @t29) @t2))) % 150.98/151.30 (define @t142 () (lambda (@list @t1 @t97) (_ tptp.lam @t133))) % 150.98/151.30 (define @t143 () (lambda @t103 (_ tptp.var @t29))) % 150.98/151.30 (define @t144 () (lambda @t122 (forall @t139 (= @t138 (_ (_ @t114 @t137) tptp.id))))) % 150.98/151.30 (define @t145 () (@var "BOUND_VARIABLE_9397" tptp.term)) % 150.98/151.30 (define @t146 () (@var "BOUND_VARIABLE_11460" (@ho-elim-sort (-> tptp.term Bool)))) % 150.98/151.30 (define @t147 () (@const 0 (-> (@ho-elim-sort (-> tptp.term Bool)) tptp.term Bool))) % 150.98/151.30 (define @t148 () (@const 2 (-> (@ho-elim-sort (-> tptp.term tptp.term)) tptp.term tptp.term))) % 150.98/151.30 (define @t149 () (_ @t148 (@const 1 (@ho-elim-sort (-> tptp.term tptp.term))) @t5)) % 150.98/151.30 (define @t150 () (@const 6 (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)))) % 150.98/151.30 (define @t151 () (@const 7 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term))))) % 150.98/151.30 (define @t152 () (_ @t151 @t150 @t5)) % 150.98/151.30 (define @t153 () (@const 8 (-> (@ho-elim-sort (-> tptp.subst tptp.term)) tptp.subst tptp.term))) % 150.98/151.30 (define @t154 () (_ @t153 @t152 (_ (@const 5 (-> (@ho-elim-sort (-> tptp.subst tptp.subst)) tptp.subst tptp.subst)) (_ (@const 4 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.subst)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.subst)))) (@const 3 (@ho-elim-sort (-> tptp.term tptp.subst tptp.subst))) @t2) tptp.id))) % 150.98/151.30 (define @t155 () (not (_ @t147 @t146 @t2))) % 150.98/151.30 (define @t156 () (not (forall @t14 (or (not (forall @t64 (or @t155 (_ @t147 @t146 @t154)))) (_ @t147 @t146 @t149))))) % 150.98/151.30 (define @t157 () (_ @t148 (_ (@const 10 (-> (@ho-elim-sort (-> tptp.term tptp.term tptp.term)) tptp.term (@ho-elim-sort (-> tptp.term tptp.term)))) (@const 9 (@ho-elim-sort (-> tptp.term tptp.term tptp.term))) @t5) @t2)) % 150.98/151.30 (define @t158 () (_ @t147 @t146 @t5)) % 150.98/151.30 (define @t159 () (not (forall @t46 (or (not @t158) @t155 (_ @t147 @t146 @t157))))) % 150.98/151.30 (define @t160 () (@const 11 (@ho-elim-sort (-> tptp.term Bool)))) % 150.98/151.30 (define @t161 () (not (_ @t147 @t160 @t5))) % 150.98/151.30 (define @t162 () (forall (@list @t146 @t145) (or (not (forall @t14 (or @t161 @t158))) @t159 @t156 (_ @t147 @t146 @t145)))) % 150.98/151.30 (define @t163 () (@var "BOUND_VARIABLE_9372" tptp.subst)) % 150.98/151.30 (define @t164 () (@var "BOUND_VARIABLE_9370" tptp.term)) % 150.98/151.30 (define @t165 () (_ @t151 @t150 @t2)) % 150.98/151.30 (define @t166 () (not (_ @t147 @t160 @t2))) % 150.98/151.30 (define @t167 () (_ @t35 @t145)) % 150.98/151.30 (define @t168 () (tptp.lam @t5)) % 150.98/151.30 (define @t169 () (_ @t35 @t168)) % 150.98/151.30 (define @t170 () (tptp.push @t2 tptp.id)) % 150.98/151.30 (define @t171 () (tptp.sub @t5 @t170)) % 150.98/151.30 (define @t172 () (_ @t35 @t171)) % 150.98/151.30 (define @t173 () (_ @t35 @t2)) % 150.98/151.30 (define @t174 () (not @t173)) % 150.98/151.30 (define @t175 () (forall @t64 (or @t174 @t172))) % 150.98/151.30 (define @t176 () (not @t175)) % 150.98/151.30 (define @t177 () (forall @t14 (or @t176 @t169))) % 150.98/151.30 (define @t178 () (not @t177)) % 150.98/151.30 (define @t179 () (tptp.ap @t5 @t2)) % 150.98/151.30 (define @t180 () (_ @t35 @t179)) % 150.98/151.30 (define @t181 () (_ @t35 @t5)) % 150.98/151.30 (define @t182 () (forall @t46 (or (not @t181) @t174 @t180))) % 150.98/151.30 (define @t183 () (not @t182)) % 150.98/151.30 (define @t184 () (tptp.var @t5)) % 150.98/151.30 (define @t185 () (forall @t14 (or (not @t184) @t181))) % 150.98/151.30 (define @t186 () (not @t185)) % 150.98/151.30 (define @t187 () (or @t186 @t183 @t178 @t167)) % 150.98/151.30 (define @t188 () (forall (@list @t35 @t145) @t187)) % 150.98/151.30 (define @t189 () (_ @t35 (tptp.sub @t164 @t163))) % 150.98/151.30 (define @t190 () (tptp.var @t2)) % 150.98/151.30 (define @t191 () (not @t190)) % 150.98/151.30 (define @t192 () (not (forall @t64 (or @t191 (_ @t35 (tptp.sub @t2 @t163)))))) % 150.98/151.30 (define @t193 () (or @t183 @t178 @t192 @t189)) % 150.98/151.30 (define @t194 () (@list @t35 @t164 @t163)) % 150.98/151.30 (define @t195 () (tptp.sub @t5 tptp.id)) % 150.98/151.30 (define @t196 () (@list @t145)) % 150.98/151.30 (define @t197 () (forall @t196 @t187)) % 150.98/151.30 (define @t198 () (forall @t196 @t167)) % 150.98/151.30 (define @t199 () (or @t186 @t183 @t178 @t198)) % 150.98/151.30 (define @t200 () (forall @t14 @t181)) % 150.98/151.30 (define @t201 () (or @t186 @t183 @t178 @t200)) % 150.98/151.30 (define @t202 () (or @t183 @t178 @t200)) % 150.98/151.30 (define @t203 () (=> @t177 @t200)) % 150.98/151.30 (define @t204 () (=> @t182 @t203)) % 150.98/151.30 (define @t205 () (or @t176 @t48)) % 150.98/151.30 (define @t206 () (not @t50)) % 150.98/151.30 (define @t207 () (or @t206 @t75)) % 150.98/151.30 (define @t208 () (not @t36)) % 150.98/151.30 (define @t209 () (or @t208 @t206 @t49)) % 150.98/151.30 (define @t210 () (not @t34)) % 150.98/151.30 (define @t211 () (or @t210 @t36)) % 150.98/151.30 (define @t212 () (or @t192 @t189)) % 150.98/151.30 (define @t213 () (or @t183 @t178 @t212)) % 150.98/151.30 (define @t214 () (forall @t194 @t213)) % 150.98/151.30 (define @t215 () (@list @t164 @t163)) % 150.98/151.30 (define @t216 () (forall @t215 @t213)) % 150.98/151.30 (define @t217 () (forall @t215 @t212)) % 150.98/151.30 (define @t218 () (or @t183 @t178 @t217)) % 150.98/151.30 (define @t219 () (tptp.sub @t5 @t1)) % 150.98/151.30 (define @t220 () (_ @t35 @t219)) % 150.98/151.30 (define @t221 () (tptp.sub @t2 @t1)) % 150.98/151.30 (define @t222 () (_ @t35 @t221)) % 150.98/151.30 (define @t223 () (forall @t64 (or @t191 @t222))) % 150.98/151.30 (define @t224 () (not @t223)) % 150.98/151.30 (define @t225 () (forall @t12 (or @t224 @t220))) % 150.98/151.30 (define @t226 () (or @t183 @t178 @t225)) % 150.98/151.30 (define @t227 () (=> @t177 @t225)) % 150.98/151.30 (define @t228 () (or @t224 @t70)) % 150.98/151.30 (define @t229 () (not @t63)) % 150.98/151.30 (define @t230 () (or @t229 @t62)) % 150.98/151.30 (define @t231 () (= @t5 @t13)) % 150.98/151.30 (define @t232 () (@quantifiers_skolemize @t162 0)) % 150.98/151.30 (define @t233 () (_ @t147 @t232 @t5)) % 150.98/151.30 (define @t234 () (forall @t14 (or @t161 @t233))) % 150.98/151.30 (define @t235 () (@quantifiers_skolemize @t162 1)) % 150.98/151.30 (define @t236 () (_ @t147 @t232 @t235)) % 150.98/151.30 (define @t237 () (not (_ @t147 @t232 @t2))) % 150.98/151.30 (define @t238 () (forall @t14 (or (not (forall @t64 (or @t237 (_ @t147 @t232 @t154)))) (_ @t147 @t232 @t149)))) % 150.98/151.30 (define @t239 () (not @t238)) % 150.98/151.30 (define @t240 () (forall @t46 (or (not @t233) @t237 (_ @t147 @t232 @t157)))) % 150.98/151.30 (define @t241 () (not @t240)) % 150.98/151.30 (define @t242 () (not @t234)) % 150.98/151.30 (define @t243 () (or @t242 @t241 @t239 @t236)) % 150.98/151.30 (define @t244 () (@list true)) % 150.98/151.30 (define @t245 () (@list @t243)) % 150.98/151.30 (define @t246 () (forall @t64 (or @t166 (_ @t147 @t232 (_ @t153 @t165 tptp.id))))) % 150.98/151.30 (define @t247 () (@quantifiers_skolemize @t246 0)) % 150.98/151.30 (define @t248 () (@list @t247)) % 150.98/151.30 (define @t249 () (_ @t147 @t232 (_ @t153 (_ @t151 @t150 @t235) tptp.id))) % 150.98/151.30 (define @t250 () (not @t246)) % 150.98/151.30 (define @t251 () (or @t241 @t239 @t250 @t249)) % 150.98/151.30 (define @t252 () (_ @t147 @t160 @t247)) % 150.98/151.30 (define @t253 () (_ @t147 @t232 (_ @t153 (_ @t151 @t150 @t247) tptp.id))) % 150.98/151.30 (define @t254 () (not @t252)) % 150.98/151.30 (define @t255 () (or @t254 @t253)) % 150.98/151.30 (define @t256 () (@list @t255)) % 150.98/151.30 (define @t257 () (_ @t147 @t232 @t247)) % 150.98/151.30 (define @t258 () (or @t254 @t257)) % 150.98/151.30 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 150.98/151.30 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 150.98/151.30 (assume @p3 @t16) % 150.98/151.30 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t19) @t1) (_ tptp.lam (_ @t6 (_ @t18 (_ @t17 tptp.sh)))))))) % 150.98/151.30 (assume @p5 (= tptp.axclos @t23)) % 150.98/151.30 (assume @p6 (= tptp.axidl @t25)) % 150.98/151.30 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t26 @t10) @t1)))) % 150.98/151.30 (assume @p8 (= tptp.axassoc @t28)) % 150.98/151.30 (assume @p9 (= tptp.axmap (forall @t22 (= (_ (_ tptp.comp @t10) @t20) @t30)))) % 150.98/151.30 (assume @p10 (= tptp.axidr @t31)) % 150.98/151.30 (assume @p11 (= tptp.axvarshift (= @t32 tptp.id))) % 150.98/151.30 (assume @p12 (= tptp.axscons (forall @t24 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t26 @t1)) @t1)))) % 150.98/151.30 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 150.98/151.30 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t34 (_ tptp.var @t33))))) % 150.98/151.30 (assume @p15 (= tptp.ulamvarind (forall @t38 (=> (_ @t35 tptp.one) (=> (forall @t14 (=> @t34 (=> @t36 (_ @t35 @t33)))) @t37))))) % 150.98/151.30 (assume @p16 (= tptp.apinj1 (forall @t44 (=> @t43 @t39)))) % 150.98/151.30 (assume @p17 (= tptp.apinj2 (forall @t44 (=> @t43 @t45)))) % 150.98/151.30 (assume @p18 (= tptp.laminj (forall @t46 (=> (= @t19 (_ tptp.lam @t2)) @t39)))) % 150.98/151.30 (assume @p19 (= tptp.shinj (forall @t46 (=> (= @t33 (_ @t3 tptp.sh)) @t39)))) % 150.98/151.30 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t42) (not (= @t19 (_ @t41 @t42)))))) % 150.98/151.30 (assume @p21 (= tptp.apnotvar (forall @t46 (not (_ tptp.var @t9))))) % 150.98/151.30 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t19))))) % 150.98/151.30 (assume @p23 (= tptp.induction (forall @t38 (=> @t37 (=> @t52 (=> (forall @t14 (=> @t36 @t48)) @t47)))))) % 150.98/151.30 (assume @p24 (= tptp.pushprop_lem0 (forall @t56 (exists @t55 @t54)))) % 150.98/151.30 (assume @p25 (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0))))))))))))))))))))))))) % 150.98/151.30 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 150.98/151.30 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t35 @t58 @t5 @t1 @t2) (=> @t36 (_ @t58 (_ @t6 (_ @t57 @t1))))))) % 150.98/151.30 (assume @p28 (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1))))))))))))))))))))))))) % 150.98/151.30 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 150.98/151.30 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t59 (=> @t36 (=> @t54 (_ @t53 tptp.one)))))) % 150.98/151.30 (assume @p31 (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2))))))))))))))))))))))))) % 150.98/151.30 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 150.98/151.30 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t59 (=> @t54 (=> @t65 (forall @t61 (=> (_ tptp.var @t42) (=> (_ @t53 @t42) (_ @t53 (_ @t60 tptp.sh)))))))))) % 150.98/151.30 (assume @p34 (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2))))))))))))))))))))))))) % 150.98/151.30 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 150.98/151.30 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t59 (=> @t54 (=> (forall @t64 (=> @t63 @t68)) @t67))))) % 150.98/151.30 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 150.98/151.30 (assume @p38 (= tptp.pushprop (forall @t56 (=> @t65 (=> @t36 @t67))))) % 150.98/151.30 (assume @p39 (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop))))))))))))))))))))))))) % 150.98/151.30 (assume @p40 (= tptp.pushprop_lthm_orig @t69)) % 150.98/151.30 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t69))) % 150.98/151.30 (assume @p42 @t82) % 150.98/151.30 (assume @p43 (= tptp.induction2lem_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar @t83)))))))))))))))))))))))) % 150.98/151.30 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t83)))))))))) % 150.98/151.30 (assume @p45 @t88) % 150.98/151.30 (assume @p46 (= tptp.induction2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop @t89)))))))))))))))))))))))))) % 150.98/151.30 (assume @p47 @t91) % 150.98/151.30 (assume @p48 (= tptp.substmonoid (and @t28 @t25 @t31))) % 150.98/151.30 (assume @p49 (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid)))))))))))))))))))))))))))) % 150.98/151.30 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 150.98/151.30 (assume @p51 (= tptp.termmset (and @t23 @t15))) % 150.98/151.30 (assume @p52 (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 150.98/151.30 (assume @p54 (= tptp.hoasapinj1 (forall @t44 (=> @t94 @t39)))) % 150.98/151.30 (assume @p55 (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1)))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 150.98/151.30 (assume @p57 (= tptp.hoasapinj2 (forall @t44 (=> @t94 @t45)))) % 150.98/151.30 (assume @p58 (= tptp.hoasapinj2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 tptp.hoasapinj2))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 150.98/151.30 (assume @p60 (= tptp.hoaslaminj (forall @t107 (=> @t106 (forall (@list @t95) (=> (forall @t103 (= (_ (_ tptp.sub @t96) @t20) (_ (_ @t95 @t21) @t29))) (=> (= @t102 (_ @t101 (lambda @t100 @t96))) (forall @t100 (= @t99 @t96))))))))) % 150.98/151.30 (assume @p61 (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj)))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 150.98/151.30 (assume @p63 (= tptp.hoaslamnotap (forall @t107 (=> @t106 (forall @t46 (not (= (_ @t101 (lambda (@list @t1 @t42) (_ @t98 @t42))) @t108))))))) % 150.98/151.30 (assume @p64 (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 150.98/151.30 (assume @p66 (= tptp.hoaslamnotvar (forall @t107 (=> @t106 (not (_ (_ @t109 @t102) tptp.id)))))) % 150.98/151.30 (assume @p67 (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar)))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 150.98/151.30 (assume @p69 (= tptp.hoasapnotvar (forall @t46 (not (_ (_ @t109 @t108) tptp.id))))) % 150.98/151.30 (assume @p70 (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 150.98/151.30 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t112 (exists @t55 @t111)))) % 150.98/151.30 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 150.98/151.30 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t122 (=> @t121 (=> @t120 (=> @t116 (=> @t111 (forall @t14 (=> @t34 @t113))))))))) % 150.98/151.30 (assume @p75 (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t122 (=> @t121 (=> @t120 (=> @t124 (=> @t111 (forall @t46 (=> @t113 (=> @t68 (_ @t53 @t9))))))))))) % 150.98/151.30 (assume @p77 (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t64 (exists @t107 (forall @t12 (= @t99 @t66)))))) % 150.98/151.30 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 150.98/151.30 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t122 (=> @t121 (=> @t120 @t127))))) % 150.98/151.30 (assume @p81 (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2)))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 150.98/151.30 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t122 @t127))) % 150.98/151.30 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 150.98/151.30 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t112 (=> @t121 (=> @t120 (=> @t116 (forall @t14 (=> @t34 @t115)))))))) % 150.98/151.30 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t128)) % 150.98/151.30 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t128)) % 150.98/151.30 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t112 (=> @t121 (=> @t120 (=> @t124 (forall @t46 (=> @t115 (=> @t123 (_ (_ @t114 @t9) tptp.id)))))))))) % 150.98/151.30 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t129)) % 150.98/151.30 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t129)) % 150.98/151.30 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t112 (=> @t126 @t131)))) % 150.98/151.30 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 150.98/151.30 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t112 (=> (forall @t107 (=> (exists @t61 (forall @t103 (and (= @t105 (_ (_ tptp.sub (_ @t60 @t10)) @t20)) (= (_ @t60 @t30) @t104)))) @t125)) @t131)))) % 150.98/151.30 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t112 (=> @t121 (=> @t120 @t132))))) % 150.98/151.30 (assume @p95 (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3)))))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 150.98/151.30 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t112 @t132))) % 150.98/151.30 (assume @p98 (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a)))))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 150.98/151.30 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t64 (exists @t107 (= (_ @t3 @t32) @t133))))) % 150.98/151.30 (assume @p101 (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b)))))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 150.98/151.30 (assume @p103 (= tptp.hoasinduction (forall @t112 (=> @t121 (=> @t120 (=> @t116 @t134)))))) % 150.98/151.30 (assume @p104 (= tptp.hoasinduction_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar @t135)))))))))))))))))))))))))))))))))))) % 150.98/151.30 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t135))) % 150.98/151.30 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 150.98/151.30 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t112 @t134))) % 150.98/151.30 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 150.98/151.30 (assume @p109 @t136) % 150.98/151.30 (assume @p110 true) % 150.98/151.30 (step @p111 (= tptp.pushprop_p_and_p_prime @t140) :rule refl :args (@t140)) % 150.98/151.30 (step @p112 (= tptp.hoasap @t141) :rule refl :args (@t141)) % 150.98/151.30 (step @p113 (= tptp.hoaslam @t142) :rule refl :args (@t142)) % 150.98/151.30 (step @p114 (= tptp.hoasvar @t143) :rule refl :args (@t143)) % 150.98/151.30 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t144) :rule refl :args (@t144)) % 150.98/151.30 (step @p116 :rule evaluate :args ((= false true))) % 150.98/151.30 ; WARNING: add trust step for TRUST % 150.98/151.30 ; trust TRUST PREPROCESS_HO_ELIM % 150.98/151.30 (step @p117 :rule trust :premises () :args ((= (not (=> (forall @t14 (= @t5 @t195)) (=> (forall @t194 @t193) @t188))) (not (=> (forall @t14 (= @t5 (_ @t153 @t152 tptp.id))) (=> (forall (@list @t146 @t164 @t163) (or @t159 @t156 (not (forall @t64 (or @t166 (_ @t147 @t146 (_ @t153 @t165 @t163))))) (_ @t147 @t146 (_ @t153 (_ @t151 @t150 @t164) @t163)))) @t162)))))) % 150.98/151.30 (step @p118 :rule quant-merge-prenex :args ((= (forall @t38 @t197) @t188))) % 150.98/151.30 (step @p119 :rule alpha_equiv :args (@t198 (@list @t145) (@list @t5))) % 150.98/151.30 (step @p120 :rule refl :args (@t178)) % 150.98/151.30 (step @p121 :rule refl :args (@t183)) % 150.98/151.30 (step @p122 :rule refl :args (@t186)) % 150.98/151.30 (step @p123 :rule nary_cong :premises (@p122 @p121 @p120 @p119) :args (@t199)) % 150.98/151.30 (step @p124 :rule quant-miniscope-or :args ((= @t197 @t199))) % 150.98/151.30 (step @p125 :rule trans :premises (@p124 @p123)) % 150.98/151.30 (step @p126 :rule symm :premises (@p125)) % 150.98/151.30 (step @p127 :rule cong :premises (@p126) :args ((forall @t38 @t201))) % 150.98/151.30 (step @p128 :rule trans :premises (@p127 @p118)) % 150.98/151.30 (step @p129 :rule aci_norm :args ((= (or @t186 @t202) @t201))) % 150.98/151.30 (step @p130 :rule aci_norm :args ((= (or @t183 (or @t178 @t200)) @t202))) % 150.98/151.30 (step @p131 :rule bool-impl-elim :args (@t177 @t200)) % 150.98/151.30 (step @p132 :rule nary_cong :premises (@p121 @p131) :args ((or @t183 @t203))) % 150.98/151.30 (step @p133 :rule trans :premises (@p132 @p130)) % 150.98/151.30 (step @p134 :rule bool-impl-elim :args (@t182 @t203)) % 150.98/151.30 (step @p135 :rule trans :premises (@p134 @p133)) % 150.98/151.30 (step @p136 :rule nary_cong :premises (@p122 @p135) :args ((or @t186 @t204))) % 150.98/151.30 (step @p137 :rule trans :premises (@p136 @p129)) % 150.98/151.30 (step @p138 :rule bool-impl-elim :args (@t185 @t204)) % 150.98/151.30 (step @p139 :rule trans :premises (@p138 @p137)) % 150.98/151.30 (step @p140 :rule cong :premises (@p139) :args ((forall @t38 (=> @t185 @t204)))) % 150.98/151.30 (step @p141 :rule trans :premises (@p140 @p128)) % 150.98/151.30 (step @p142 :rule refl :args (@t181)) % 150.98/151.30 (step @p143 :rule refl :args (@t36)) % 150.98/151.30 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t36 @t181))) % 150.98/151.30 (step @p145 :rule symm :premises (@p144)) % 150.98/151.30 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 150.98/151.30 (step @p147 :rule cong :premises (@p146) :args (@t47)) % 150.98/151.30 (step @p148 :rule refl :args ((_ @t35 @t19))) % 150.98/151.30 (step @p149 :rule refl :args (@t168)) % 150.98/151.30 (step @p150 :rule cong :premises (@p149) :args (@t169)) % 150.98/151.30 (step @p151 :rule trans :premises (@p150 @p148)) % 150.98/151.30 (step @p152 :rule refl :args (@t35)) % 150.98/151.30 (step @p153 :rule ho_cong :premises (@p152 @p149)) % 150.98/151.30 (step @p154 :rule cong :premises (@p153 @p151) :args ((= (_ @t35 @t168) @t169))) % 150.98/151.30 (step @p155 :rule symm :premises (@p154)) % 150.98/151.30 (step @p156 :rule refl :args (@t48)) % 150.98/151.30 (step @p157 :rule eq_resolve :premises (@p156 @p155)) % 150.98/151.30 (step @p158 :rule refl :args (@t19)) % 150.98/151.30 (step @p159 :rule cong :premises (@p158 @p149) :args ((= @t19 @t168))) % 150.98/151.30 (step @p160 :rule symm :premises (@p159)) % 150.98/151.30 (step @p161 :rule eq_resolve :premises (@p158 @p160)) % 150.98/151.30 (step @p162 :rule ho_cong :premises (@p152 @p161)) % 150.98/151.30 (step @p163 :rule trans :premises (@p162 @p157)) % 150.98/151.30 (step @p164 :rule refl :args (@t176)) % 150.98/151.30 (step @p165 :rule nary_cong :premises (@p164 @p163) :args (@t205)) % 150.98/151.30 (step @p166 :rule cong :premises (@p165) :args ((forall @t14 @t205))) % 150.98/151.30 (step @p167 :rule bool-impl-elim :args (@t175 @t48)) % 150.98/151.30 (step @p168 :rule cong :premises (@p167) :args ((forall @t14 (=> @t175 @t48)))) % 150.98/151.30 (step @p169 :rule trans :premises (@p168 @p166)) % 150.98/151.30 (step @p170 :rule refl :args (@t48)) % 150.98/151.30 (step @p171 :rule refl :args ((_ @t35 @t74))) % 150.98/151.30 (step @p172 :rule refl :args ((tptp.sub @t5 @t73))) % 150.98/151.30 (step @p173 :rule refl :args (@t170)) % 150.98/151.30 (step @p174 :rule refl :args (@t5)) % 150.98/151.30 (step @p175 :rule cong :premises (@p174 @p173) :args (@t171)) % 150.98/151.30 (step @p176 :rule trans :premises (@p175 @p172)) % 150.98/151.30 (step @p177 :rule cong :premises (@p176) :args (@t172)) % 150.98/151.30 (step @p178 :rule trans :premises (@p177 @p171)) % 150.98/151.30 (step @p179 :rule ho_cong :premises (@p152 @p176)) % 150.98/151.30 (step @p180 :rule cong :premises (@p179 @p178) :args ((= (_ @t35 @t171) @t172))) % 150.98/151.30 (step @p181 :rule symm :premises (@p180)) % 150.98/151.30 (step @p182 :rule refl :args (@t75)) % 150.98/151.30 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 150.98/151.30 (step @p184 :rule refl :args (@t6)) % 150.98/151.30 (step @p185 :rule ho_cong :premises (@p184 @p173)) % 150.98/151.30 (step @p186 :rule cong :premises (@p185 @p176) :args ((= (_ @t6 @t170) @t171))) % 150.98/151.30 (step @p187 :rule symm :premises (@p186)) % 150.98/151.30 (step @p188 :rule refl :args (@t74)) % 150.98/151.30 (step @p189 :rule eq_resolve :premises (@p188 @p187)) % 150.98/151.30 (step @p190 :rule refl :args (@t73)) % 150.98/151.30 (step @p191 :rule cong :premises (@p190 @p173) :args ((= @t73 @t170))) % 150.98/151.30 (step @p192 :rule symm :premises (@p191)) % 150.98/151.30 (step @p193 :rule eq_resolve :premises (@p190 @p192)) % 150.98/151.30 (step @p194 :rule ho_cong :premises (@p184 @p193)) % 150.98/151.30 (step @p195 :rule trans :premises (@p194 @p189)) % 150.98/151.30 (step @p196 :rule ho_cong :premises (@p152 @p195)) % 150.98/151.30 (step @p197 :rule trans :premises (@p196 @p183)) % 150.98/151.30 (step @p198 :rule refl :args (@t173)) % 150.98/151.30 (step @p199 :rule refl :args (@t50)) % 150.98/151.30 (step @p200 :rule cong :premises (@p199 @p198) :args ((= @t50 @t173))) % 150.98/151.30 (step @p201 :rule symm :premises (@p200)) % 150.98/151.30 (step @p202 :rule eq_resolve :premises (@p199 @p201)) % 150.98/151.30 (step @p203 :rule cong :premises (@p202) :args (@t206)) % 150.98/151.30 (step @p204 :rule nary_cong :premises (@p203 @p197) :args (@t207)) % 150.98/151.30 (step @p205 :rule cong :premises (@p204) :args ((forall @t64 @t207))) % 150.98/151.30 (step @p206 :rule bool-impl-elim :args (@t50 @t75)) % 150.98/151.30 (step @p207 :rule cong :premises (@p206) :args (@t76)) % 150.98/151.30 (step @p208 :rule trans :premises (@p207 @p205)) % 150.98/151.30 (step @p209 :rule cong :premises (@p208 @p170) :args (@t77)) % 150.98/151.30 (step @p210 :rule cong :premises (@p209) :args (@t78)) % 150.98/151.30 (step @p211 :rule trans :premises (@p210 @p169)) % 150.98/151.30 (step @p212 :rule cong :premises (@p211 @p147) :args (@t84)) % 150.98/151.30 (step @p213 :rule refl :args ((_ @t35 @t9))) % 150.98/151.30 (step @p214 :rule refl :args (@t179)) % 150.98/151.30 (step @p215 :rule cong :premises (@p214) :args (@t180)) % 150.98/151.30 (step @p216 :rule trans :premises (@p215 @p213)) % 150.98/151.30 (step @p217 :rule ho_cong :premises (@p152 @p214)) % 150.98/151.30 (step @p218 :rule cong :premises (@p217 @p216) :args ((= (_ @t35 @t179) @t180))) % 150.98/151.30 (step @p219 :rule symm :premises (@p218)) % 150.98/151.30 (step @p220 :rule refl :args (@t49)) % 150.98/151.30 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 150.98/151.30 (step @p222 :rule refl :args (@t9)) % 150.98/151.30 (step @p223 :rule cong :premises (@p222 @p214) :args ((= @t9 @t179))) % 150.98/151.30 (step @p224 :rule symm :premises (@p223)) % 150.98/151.30 (step @p225 :rule eq_resolve :premises (@p222 @p224)) % 150.98/151.30 (step @p226 :rule ho_cong :premises (@p152 @p225)) % 150.98/151.30 (step @p227 :rule trans :premises (@p226 @p221)) % 150.98/151.30 (step @p228 :rule cong :premises (@p146) :args (@t208)) % 150.98/151.30 (step @p229 :rule nary_cong :premises (@p228 @p203 @p227) :args (@t209)) % 150.98/151.30 (step @p230 :rule cong :premises (@p229) :args ((forall @t46 @t209))) % 150.98/151.30 (step @p231 :rule aci_norm :args ((= (or @t208 (or @t206 @t49)) @t209))) % 150.98/151.30 (step @p232 :rule bool-impl-elim :args (@t50 @t49)) % 150.98/151.30 (step @p233 :rule refl :args (@t208)) % 150.98/151.30 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((or @t208 @t51))) % 150.98/151.30 (step @p235 :rule trans :premises (@p234 @p231)) % 150.98/151.30 (step @p236 :rule bool-impl-elim :args (@t36 @t51)) % 150.98/151.30 (step @p237 :rule trans :premises (@p236 @p235)) % 150.98/151.30 (step @p238 :rule cong :premises (@p237) :args (@t52)) % 150.98/151.30 (step @p239 :rule trans :premises (@p238 @p230)) % 150.98/151.30 (step @p240 :rule cong :premises (@p239 @p212) :args (@t85)) % 150.98/151.30 (step @p241 :rule refl :args (@t184)) % 150.98/151.30 (step @p242 :rule refl :args (@t34)) % 150.98/151.30 (step @p243 :rule cong :premises (@p242 @p241) :args ((= @t34 @t184))) % 150.98/151.30 (step @p244 :rule symm :premises (@p243)) % 150.98/151.30 (step @p245 :rule eq_resolve :premises (@p242 @p244)) % 150.98/151.30 (step @p246 :rule cong :premises (@p245) :args (@t210)) % 150.98/151.30 (step @p247 :rule nary_cong :premises (@p246 @p146) :args (@t211)) % 150.98/151.30 (step @p248 :rule cong :premises (@p247) :args ((forall @t14 @t211))) % 150.98/151.30 (step @p249 :rule bool-impl-elim :args (@t34 @t36)) % 150.98/151.30 (step @p250 :rule cong :premises (@p249) :args (@t37)) % 150.98/151.30 (step @p251 :rule trans :premises (@p250 @p248)) % 150.98/151.30 (step @p252 :rule cong :premises (@p251 @p240) :args (@t86)) % 150.98/151.30 (step @p253 :rule cong :premises (@p252) :args (@t87)) % 150.98/151.30 (step @p254 :rule trans :premises (@p253 @p141)) % 150.98/151.30 (step @p255 :rule refl :args (tptp.induction2)) % 150.98/151.30 (step @p256 :rule cong :premises (@p255 @p254) :args (@t88)) % 150.98/151.30 (step @p257 :rule eq_resolve :premises (@p45 @p256)) % 150.98/151.30 (step @p258 :rule aci_norm :args ((= @t213 @t193))) % 150.98/151.30 (step @p259 :rule cong :premises (@p258) :args (@t214)) % 150.98/151.30 (step @p260 :rule quant-merge-prenex :args ((= (forall @t38 @t216) @t214))) % 150.98/151.30 (step @p261 :rule alpha_equiv :args (@t217 (@list @t164 @t163) (@list @t5 @t1))) % 150.98/151.30 (step @p262 :rule nary_cong :premises (@p121 @p120 @p261) :args (@t218)) % 150.98/151.30 (step @p263 :rule quant-miniscope-or :args ((= @t216 @t218))) % 150.98/151.30 (step @p264 :rule trans :premises (@p263 @p262)) % 150.98/151.30 (step @p265 :rule symm :premises (@p264)) % 150.98/151.30 (step @p266 :rule cong :premises (@p265) :args ((forall @t38 @t226))) % 150.98/151.30 (step @p267 :rule trans :premises (@p266 @p260)) % 150.98/151.30 (step @p268 :rule trans :premises (@p267 @p259)) % 150.98/151.30 (step @p269 :rule aci_norm :args ((= (or @t183 (or @t178 @t225)) @t226))) % 150.98/151.30 (step @p270 :rule bool-impl-elim :args (@t177 @t225)) % 150.98/151.30 (step @p271 :rule nary_cong :premises (@p121 @p270) :args ((or @t183 @t227))) % 150.98/151.30 (step @p272 :rule trans :premises (@p271 @p269)) % 150.98/151.30 (step @p273 :rule bool-impl-elim :args (@t182 @t227)) % 150.98/151.30 (step @p274 :rule trans :premises (@p273 @p272)) % 150.98/151.30 (step @p275 :rule cong :premises (@p274) :args ((forall @t38 (=> @t182 @t227)))) % 150.98/151.30 (step @p276 :rule trans :premises (@p275 @p268)) % 150.98/151.30 (step @p277 :rule refl :args ((_ @t35 @t7))) % 150.98/151.30 (step @p278 :rule refl :args (@t219)) % 150.98/151.30 (step @p279 :rule cong :premises (@p278) :args (@t220)) % 150.98/151.30 (step @p280 :rule trans :premises (@p279 @p277)) % 150.98/151.30 (step @p281 :rule ho_cong :premises (@p152 @p278)) % 150.98/151.30 (step @p282 :rule cong :premises (@p281 @p280) :args ((= (_ @t35 @t219) @t220))) % 150.98/151.30 (step @p283 :rule symm :premises (@p282)) % 150.98/151.30 (step @p284 :rule refl :args (@t70)) % 150.98/151.30 (step @p285 :rule eq_resolve :premises (@p284 @p283)) % 150.98/151.30 (step @p286 :rule refl :args (@t7)) % 150.98/151.30 (step @p287 :rule cong :premises (@p286 @p278) :args ((= @t7 @t219))) % 150.98/151.30 (step @p288 :rule symm :premises (@p287)) % 150.98/151.30 (step @p289 :rule eq_resolve :premises (@p286 @p288)) % 150.98/151.30 (step @p290 :rule ho_cong :premises (@p152 @p289)) % 150.98/151.30 (step @p291 :rule trans :premises (@p290 @p285)) % 150.98/151.30 (step @p292 :rule refl :args (@t224)) % 150.98/151.30 (step @p293 :rule nary_cong :premises (@p292 @p291) :args (@t228)) % 150.98/151.30 (step @p294 :rule cong :premises (@p293) :args ((forall @t12 @t228))) % 150.98/151.30 (step @p295 :rule bool-impl-elim :args (@t223 @t70)) % 150.98/151.30 (step @p296 :rule cong :premises (@p295) :args ((forall @t12 (=> @t223 @t70)))) % 150.98/151.30 (step @p297 :rule trans :premises (@p296 @p294)) % 150.98/151.30 (step @p298 :rule refl :args (@t70)) % 150.98/151.30 (step @p299 :rule refl :args ((_ @t35 @t4))) % 150.98/151.30 (step @p300 :rule refl :args (@t221)) % 150.98/151.30 (step @p301 :rule cong :premises (@p300) :args (@t222)) % 150.98/151.30 (step @p302 :rule trans :premises (@p301 @p299)) % 150.98/151.30 (step @p303 :rule ho_cong :premises (@p152 @p300)) % 150.98/151.30 (step @p304 :rule cong :premises (@p303 @p302) :args ((= (_ @t35 @t221) @t222))) % 150.98/151.30 (step @p305 :rule symm :premises (@p304)) % 150.98/151.30 (step @p306 :rule refl :args (@t62)) % 150.98/151.30 (step @p307 :rule eq_resolve :premises (@p306 @p305)) % 150.98/151.30 (step @p308 :rule refl :args (@t4)) % 150.98/151.30 (step @p309 :rule cong :premises (@p308 @p300) :args ((= @t4 @t221))) % 150.98/151.30 (step @p310 :rule symm :premises (@p309)) % 150.98/151.30 (step @p311 :rule eq_resolve :premises (@p308 @p310)) % 150.98/151.30 (step @p312 :rule ho_cong :premises (@p152 @p311)) % 150.98/151.30 (step @p313 :rule trans :premises (@p312 @p307)) % 150.98/151.30 (step @p314 :rule refl :args (@t190)) % 150.98/151.30 (step @p315 :rule refl :args (@t63)) % 150.98/151.30 (step @p316 :rule cong :premises (@p315 @p314) :args ((= @t63 @t190))) % 150.98/151.30 (step @p317 :rule symm :premises (@p316)) % 150.98/151.30 (step @p318 :rule eq_resolve :premises (@p315 @p317)) % 150.98/151.30 (step @p319 :rule cong :premises (@p318) :args (@t229)) % 150.98/151.30 (step @p320 :rule nary_cong :premises (@p319 @p313) :args (@t230)) % 150.98/151.30 (step @p321 :rule cong :premises (@p320) :args ((forall @t64 @t230))) % 150.98/151.30 (step @p322 :rule bool-impl-elim :args (@t63 @t62)) % 150.98/151.30 (step @p323 :rule cong :premises (@p322) :args (@t65)) % 150.98/151.30 (step @p324 :rule trans :premises (@p323 @p321)) % 150.98/151.30 (step @p325 :rule cong :premises (@p324 @p298) :args (@t71)) % 150.98/151.30 (step @p326 :rule cong :premises (@p325) :args (@t72)) % 150.98/151.30 (step @p327 :rule trans :premises (@p326 @p297)) % 150.98/151.30 (step @p328 :rule cong :premises (@p211 @p327) :args (@t79)) % 150.98/151.30 (step @p329 :rule cong :premises (@p239 @p328) :args (@t80)) % 150.98/151.30 (step @p330 :rule cong :premises (@p329) :args (@t81)) % 150.98/151.30 (step @p331 :rule trans :premises (@p330 @p276)) % 150.98/151.30 (step @p332 :rule refl :args (tptp.induction2lem)) % 150.98/151.30 (step @p333 :rule cong :premises (@p332 @p331) :args (@t82)) % 150.98/151.30 (step @p334 :rule eq_resolve :premises (@p42 @p333)) % 150.98/151.30 (step @p335 :rule cong :premises (@p334 @p257) :args (@t89)) % 150.98/151.30 (step @p336 :rule refl :args (@t195)) % 150.98/151.30 (step @p337 :rule refl :args (@t13)) % 150.98/151.30 (step @p338 :rule cong :premises (@p337 @p336) :args ((= @t13 @t195))) % 150.98/151.30 (step @p339 :rule symm :premises (@p338)) % 150.98/151.30 (step @p340 :rule eq_resolve :premises (@p337 @p339)) % 150.98/151.30 (step @p341 :rule cong :premises (@p174 @p340) :args (@t231)) % 150.98/151.30 (step @p342 :rule cong :premises (@p341) :args ((forall @t14 @t231))) % 150.98/151.30 (step @p343 :rule eq-symm :args (@t13 @t5)) % 150.98/151.30 (step @p344 :rule cong :premises (@p343) :args (@t15)) % 150.98/151.30 (step @p345 :rule trans :premises (@p344 @p342)) % 150.98/151.30 (step @p346 :rule refl :args (tptp.axvarid)) % 150.98/151.30 (step @p347 :rule cong :premises (@p346 @p345) :args (@t16)) % 150.98/151.30 (step @p348 :rule eq_resolve :premises (@p3 @p347)) % 150.98/151.30 (step @p349 :rule cong :premises (@p348 @p335) :args (@t90)) % 150.98/151.30 (step @p350 :rule refl :args (tptp.induction2_lthm)) % 150.98/151.30 (step @p351 :rule cong :premises (@p350 @p349) :args (@t91)) % 150.98/151.30 (step @p352 :rule eq_resolve :premises (@p47 @p351)) % 150.98/151.30 (step @p353 :rule cong :premises (@p352) :args (@t136)) % 150.98/151.30 (step @p354 :rule trans :premises (@p353 @p117)) % 150.98/151.30 (step @p355 :rule eq_resolve :premises (@p109 @p354)) % 150.98/151.30 (step @p356 :rule not_implies_elim2 :premises (@p355)) % 150.98/151.30 (step @p357 :rule not_implies_elim2 :premises (@p356)) % 150.98/151.30 (step @p358 :rule skolemize :premises (@p357)) % 150.98/151.30 (step @p359 :rule bool-double-not-elim :args (@t234)) % 150.98/151.30 (step @p360 :rule refl :args (@t243)) % 150.98/151.30 (step @p361 :rule nary_cong :premises (@p360 @p359) :args ((or @t243 (not @t242)))) % 150.98/151.30 (step @p362 :rule cnf_or_neg :args (@t243 0)) % 150.98/151.30 (step @p363 :rule eq_resolve :premises (@p362 @p361)) % 150.98/151.30 (step @p364 :rule reordering :premises (@p363) :args ((or @t234 @t243))) % 150.98/151.30 (step @p365 :rule chain_m_resolution :premises (@p364 @p358) :args (@t234 @t244 @t245)) % 150.98/151.30 (step @p366 :rule instantiate :premises (@p365) :args (@t248)) % 150.98/151.30 (step @p367 :rule not_implies_elim1 :premises (@p356)) % 150.98/151.30 (step @p368 :rule instantiate :premises (@p367) :args ((@list @t232 @t235 tptp.id))) % 150.98/151.30 (step @p369 :rule cnf_or_neg :args (@t243 3)) % 150.98/151.30 (step @p370 :rule chain_m_resolution :premises (@p369 @p358) :args ((not @t236) @t244 @t245)) % 150.98/151.30 (step @p371 :rule false_intro :premises (@p370)) % 150.98/151.30 (step @p372 :rule not_implies_elim1 :premises (@p355)) % 150.98/151.30 (step @p373 :rule instantiate :premises (@p372) :args ((@list @t235))) % 150.98/151.30 (step @p374 :rule symm :premises (@p373)) % 150.98/151.30 (step @p375 :rule refl :args (@t232)) % 150.98/151.30 (step @p376 :rule cong :premises (@p375 @p374) :args (@t249)) % 150.98/151.30 (step @p377 :rule trans :premises (@p376 @p371)) % 150.98/151.30 (step @p378 :rule false_elim :premises (@p377)) % 150.98/151.30 (step @p379 :rule bool-double-not-elim :args (@t238)) % 150.98/151.30 (step @p380 :rule nary_cong :premises (@p360 @p379) :args ((or @t243 (not @t239)))) % 150.98/151.30 (step @p381 :rule cnf_or_neg :args (@t243 2)) % 150.98/151.30 (step @p382 :rule eq_resolve :premises (@p381 @p380)) % 150.98/151.30 (step @p383 :rule reordering :premises (@p382) :args ((or @t238 @t243))) % 150.98/151.30 (step @p384 :rule chain_m_resolution :premises (@p383 @p358) :args (@t238 @t244 @t245)) % 150.98/151.30 (step @p385 :rule bool-double-not-elim :args (@t240)) % 150.98/151.30 (step @p386 :rule nary_cong :premises (@p360 @p385) :args ((or @t243 (not @t241)))) % 150.98/151.30 (step @p387 :rule cnf_or_neg :args (@t243 1)) % 150.98/151.30 (step @p388 :rule eq_resolve :premises (@p387 @p386)) % 150.98/151.30 (step @p389 :rule reordering :premises (@p388) :args ((or @t240 @t243))) % 150.98/151.30 (step @p390 :rule chain_m_resolution :premises (@p389 @p358) :args (@t240 @t244 @t245)) % 150.98/151.30 (step @p391 :rule cnf_or_pos :args (@t251)) % 150.98/151.30 (step @p392 :rule reordering :premises (@p391) :args ((or @t241 @t239 @t250 @t249 (not @t251)))) % 150.98/151.30 (step @p393 :rule chain_m_resolution :premises (@p392 @p390 @p384 @p378 @p368) :args (@t250 (@list false false true false) (@list @t240 @t238 @t249 @t251))) % 150.98/151.30 (step @p394 :rule skolemize :premises (@p393)) % 150.98/151.30 (step @p395 :rule bool-double-not-elim :args (@t252)) % 150.98/151.30 (step @p396 :rule refl :args (@t255)) % 150.98/151.30 (step @p397 :rule nary_cong :premises (@p396 @p395) :args ((or @t255 (not @t254)))) % 150.98/151.30 (step @p398 :rule cnf_or_neg :args (@t255 0)) % 150.98/151.30 (step @p399 :rule eq_resolve :premises (@p398 @p397)) % 150.98/151.30 (step @p400 :rule reordering :premises (@p399) :args ((or @t252 @t255))) % 150.98/151.30 (step @p401 :rule chain_m_resolution :premises (@p400 @p394) :args (@t252 @t244 @t256)) % 150.98/151.30 (step @p402 :rule cnf_or_pos :args (@t258)) % 150.98/151.30 (step @p403 :rule reordering :premises (@p402) :args ((or @t254 @t257 (not @t258)))) % 150.98/151.30 (step @p404 :rule chain_m_resolution :premises (@p403 @p401 @p366) :args (@t257 (@list false false) (@list @t252 @t258))) % 150.98/151.30 (step @p405 :rule true_intro :premises (@p404)) % 150.98/151.30 (step @p406 :rule instantiate :premises (@p372) :args (@t248)) % 150.98/151.30 (step @p407 :rule symm :premises (@p406)) % 150.98/151.30 (step @p408 :rule cong :premises (@p375 @p407) :args (@t253)) % 150.98/151.30 (step @p409 :rule cnf_or_neg :args (@t255 1)) % 150.98/151.30 (step @p410 :rule chain_m_resolution :premises (@p409 @p394) :args ((not @t253) @t244 @t256)) % 150.98/151.30 (step @p411 :rule false_intro :premises (@p410)) % 150.98/151.30 (step @p412 :rule symm :premises (@p411)) % 150.98/151.30 (step @p413 :rule trans :premises (@p412 @p408 @p405)) % 150.98/151.30 (step @p414 false :rule eq_resolve :premises (@p413 @p116)) % 150.98/151.30 ) % 150.98/151.30 % SZS output end Proof % 150.98/151.30 % cvc5 exiting %------------------------------------------------------------------------------