%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n023.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 09:07:15 AM UTC 2026 % Result : Theorem 170.50s 170.81s % Output : Proof 170.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % 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 : n023.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 : Tue Jun 2 23:03:13 EDT 2026 % 0.16/0.35 % CPUTime : % 0.38/0.56 %----Proving TH0 % 170.50/170.81 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 170.50/170.81 --- 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... % 170.50/170.81 --- 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... % 170.50/170.81 --- Run --ho-elim --full-saturate-quant at 18s... % 170.50/170.81 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 170.50/170.81 % SZS status Theorem % 170.50/170.81 % SZS output start Proof % 170.50/170.81 ( % 170.50/170.81 (declare-sort tptp.term 0) % 170.50/170.81 (declare-sort tptp.subst 0) % 170.50/170.81 (declare-sort tptp.d_term 0) % 170.50/170.81 (declare-sort tptp.d_subst 0) % 170.50/170.81 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 170.50/170.81 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 170.50/170.81 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 170.50/170.81 (declare-const tptp.pushprop_lem1v2 Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem1_gthm Bool) % 170.50/170.81 (declare-const tptp.axmap Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem0_gthm Bool) % 170.50/170.81 (declare-const tptp.shinj Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem1v2 Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 170.50/170.81 (declare-const tptp.induction2lem Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 170.50/170.81 (declare-const tptp.axvarshift Bool) % 170.50/170.81 (declare-const tptp.hoasapinj2 Bool) % 170.50/170.81 (declare-const tptp.hoasapnotvar_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasapinj1 Bool) % 170.50/170.81 (declare-const tptp.ulamvar1 Bool) % 170.50/170.81 (declare-const tptp.induction2lem_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 170.50/170.81 (declare-const tptp.apnotvar Bool) % 170.50/170.81 (declare-const tptp.pushprop_lthm_orig Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 170.50/170.81 (declare-const tptp.hoaslaminj Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3aaa Bool) % 170.50/170.81 (declare-const tptp.induction2lem_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3 Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem2 Bool) % 170.50/170.81 (declare-const tptp.termmset_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem1 Bool) % 170.50/170.81 (declare-const tptp.hoaslamnotap_lthm Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasapnotvar Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem0 Bool) % 170.50/170.81 (declare-const tptp.hoasinduction Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_gthm Bool) % 170.50/170.81 (declare-const tptp.axapp Bool) % 170.50/170.81 (declare-const tptp.hoaslamnotvar_lthm Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 170.50/170.81 (declare-const tptp.ulamvarind Bool) % 170.50/170.81 (declare-const tptp.induction Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 170.50/170.81 (declare-const tptp.termmset_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3aa Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 170.50/170.81 (declare-const tptp.hoaslamnotap_gthm Bool) % 170.50/170.81 (declare-const tptp.hoaslamnotvar_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem2v2 Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 170.50/170.81 (declare-const tptp.axclos Bool) % 170.50/170.81 (declare-const tptp.axassoc Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem2v2 Bool) % 170.50/170.81 (declare-const tptp.pushprop_lthm Bool) % 170.50/170.81 (declare-const tptp.apinj2 Bool) % 170.50/170.81 (declare-const tptp.apinj1 Bool) % 170.50/170.81 (declare-const tptp.hoasapinj2_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3v2a Bool) % 170.50/170.81 (declare-const tptp.hoasapinj1_lthm Bool) % 170.50/170.81 (declare-const tptp.hoaslaminj_lthm Bool) % 170.50/170.81 (declare-const tptp.axvarcons Bool) % 170.50/170.81 (declare-const tptp.axscons Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 170.50/170.81 (declare-const tptp.d_one tptp.d_term) % 170.50/170.81 (declare-const tptp.hoaslamnotap Bool) % 170.50/170.81 (declare-const tptp.ulamvarsh Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem3v2 Bool) % 170.50/170.81 (declare-const tptp.axshiftcons Bool) % 170.50/170.81 (declare-const tptp.id tptp.subst) % 170.50/170.81 (declare-const tptp.pushprop_lem1_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 170.50/170.81 (declare-const tptp.pushprop_lem0_lthm Bool) % 170.50/170.81 (declare-const tptp.one tptp.term) % 170.50/170.81 (declare-const tptp.substmonoid_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3v2 Bool) % 170.50/170.81 (declare-const tptp.sh tptp.subst) % 170.50/170.81 (declare-const tptp.termmset Bool) % 170.50/170.81 (declare-const tptp.induction2 Bool) % 170.50/170.81 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 170.50/170.81 (declare-const tptp.lam (-> tptp.term tptp.term)) % 170.50/170.81 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 170.50/170.81 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 170.50/170.81 (declare-const tptp.axvarid Bool) % 170.50/170.81 (declare-const tptp.d_id tptp.d_subst) % 170.50/170.81 (declare-const tptp.var (-> tptp.term Bool)) % 170.50/170.81 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 170.50/170.81 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 170.50/170.81 (declare-const tptp.hoasapnotvar_lthm Bool) % 170.50/170.81 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 170.50/170.81 (declare-const tptp.hoasinduction_lthm_3 Bool) % 170.50/170.81 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 170.50/170.81 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 170.50/170.81 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 170.50/170.81 (declare-const tptp.induction2_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3a Bool) % 170.50/170.81 (declare-const tptp.lamnotvar Bool) % 170.50/170.81 (declare-const tptp.substmonoid Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3b Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 170.50/170.81 (declare-const tptp.pushprop Bool) % 170.50/170.81 (declare-const tptp.substmonoid_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 170.50/170.81 (declare-const tptp.induction2_lthm Bool) % 170.50/170.81 (declare-const tptp.hoaslaminj_gthm Bool) % 170.50/170.81 (declare-const tptp.axidl Bool) % 170.50/170.81 (declare-const tptp.hoaslamnotvar Bool) % 170.50/170.81 (declare-const tptp.hoasapinj1_gthm Bool) % 170.50/170.81 (declare-const tptp.lamnotap Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasapinj2_gthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 170.50/170.81 (declare-const tptp.axabs Bool) % 170.50/170.81 (declare-const tptp.pushprop_gthm Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem0 Bool) % 170.50/170.81 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 170.50/170.81 (declare-const tptp.laminj Bool) % 170.50/170.81 (declare-const tptp.pushprop_lem1 Bool) % 170.50/170.81 (declare-const tptp.axidr Bool) % 170.50/170.81 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 170.50/170.81 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 170.50/170.81 (define @t3 () (_ @t2 tptp.id)) % 170.50/170.81 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 170.50/170.81 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 170.50/170.81 (define @t6 () (_ tptp.lam @t5)) % 170.50/170.81 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 170.50/170.81 (define @t8 () (@var "A" tptp.term)) % 170.50/170.81 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 170.50/170.81 (define @t10 () (not @t9)) % 170.50/170.81 (define @t11 () (@list @t8)) % 170.50/170.81 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 170.50/170.81 (define @t13 () (@var "N" tptp.subst)) % 170.50/170.81 (define @t14 () (_ tptp.sub @t8)) % 170.50/170.81 (define @t15 () (_ @t14 @t13)) % 170.50/170.81 (define @t16 () (@var "M" tptp.subst)) % 170.50/170.81 (define @t17 () (_ tptp.comp @t16)) % 170.50/170.81 (define @t18 () (_ @t17 @t13)) % 170.50/170.81 (define @t19 () (_ (_ @t4 @t16) @t8)) % 170.50/170.81 (define @t20 () (@list @t16 @t8 @t13)) % 170.50/170.81 (define @t21 () (not (forall @t20 (= (_ (_ tptp.sub @t19) @t13) (_ (_ @t4 @t18) @t15))))) % 170.50/170.81 (define @t22 () (@list @t4)) % 170.50/170.81 (define @t23 () (not (forall @t22 (or @t21 @t12 @t7)))) % 170.50/170.81 (define @t24 () (@var "B" tptp.term)) % 170.50/170.81 (define @t25 () (_ @t14 tptp.id)) % 170.50/170.81 (define @t26 () (_ tptp.ap @t25)) % 170.50/170.81 (define @t27 () (_ @t26 @t24)) % 170.50/170.81 (define @t28 () (_ (_ @t3 @t27) tptp.id)) % 170.50/170.81 (define @t29 () (_ (_ @t3 @t24) tptp.id)) % 170.50/170.81 (define @t30 () (not @t29)) % 170.50/170.81 (define @t31 () (or @t10 @t30 @t28)) % 170.50/170.81 (define @t32 () (@list @t8 @t24)) % 170.50/170.81 (define @t33 () (forall @t32 @t31)) % 170.50/170.81 (define @t34 () (not @t33)) % 170.50/170.81 (define @t35 () (@var "K" tptp.subst)) % 170.50/170.81 (define @t36 () (_ (_ tptp.comp @t35) @t13)) % 170.50/170.81 (define @t37 () (_ (_ @t2 @t16) @t8)) % 170.50/170.81 (define @t38 () (_ @t37 @t36)) % 170.50/170.81 (define @t39 () (_ @t14 @t35)) % 170.50/170.81 (define @t40 () (_ @t17 @t35)) % 170.50/170.81 (define @t41 () (_ (_ (_ @t2 @t40) @t39) @t13)) % 170.50/170.81 (define @t42 () (not @t41)) % 170.50/170.81 (define @t43 () (or @t42 @t38)) % 170.50/170.81 (define @t44 () (@list @t16 @t8 @t13 @t35)) % 170.50/170.81 (define @t45 () (forall @t44 @t43)) % 170.50/170.81 (define @t46 () (not @t45)) % 170.50/170.81 (define @t47 () (not @t38)) % 170.50/170.81 (define @t48 () (or @t47 @t41)) % 170.50/170.81 (define @t49 () (forall @t44 @t48)) % 170.50/170.81 (define @t50 () (not @t49)) % 170.50/170.81 (define @t51 () (forall (@list @t2 @t1) (or @t50 @t46 (not (forall @t11 (or (not (_ tptp.var @t25)) @t9))) @t34 @t23 (_ (_ @t3 @t1) tptp.id)))) % 170.50/170.81 (define @t52 () (@var "Bound_variable_2931" tptp.term)) % 170.50/170.81 (define @t53 () (@var "Q" (-> tptp.term Bool))) % 170.50/170.81 (define @t54 () (_ tptp.push @t24)) % 170.50/170.81 (define @t55 () (_ @t54 tptp.id)) % 170.50/170.81 (define @t56 () (_ @t53 @t24)) % 170.50/170.81 (define @t57 () (not @t56)) % 170.50/170.81 (define @t58 () (@list @t24)) % 170.50/170.81 (define @t59 () (@var "X" tptp.term)) % 170.50/170.81 (define @t60 () (_ (_ @t3 @t59) tptp.id)) % 170.50/170.81 (define @t61 () (_ @t53 @t59)) % 170.50/170.81 (define @t62 () (= @t61 @t60)) % 170.50/170.81 (define @t63 () (@list @t59)) % 170.50/170.81 (define @t64 () (forall @t63 @t62)) % 170.50/170.81 (define @t65 () (not @t64)) % 170.50/170.81 (define @t66 () (forall (@list @t2 @t53 @t52) (or @t23 @t65 (not (forall @t58 (or @t57 (_ @t53 (_ (_ tptp.sub @t52) @t55))))) (_ @t53 (_ tptp.lam @t52))))) % 170.50/170.81 (define @t67 () (forall @t11 (= @t8 @t25))) % 170.50/170.81 (define @t68 () (@var "Bound_variable_2367" tptp.term)) % 170.50/170.81 (define @t69 () (@var "P" (-> tptp.term Bool))) % 170.50/170.81 (define @t70 () (_ tptp.lam @t8)) % 170.50/170.81 (define @t71 () (_ @t69 @t70)) % 170.50/170.81 (define @t72 () (not (_ @t69 @t24))) % 170.50/170.81 (define @t73 () (not (forall @t11 (or (not (forall @t58 (or @t72 (_ @t69 (_ @t14 @t55))))) @t71)))) % 170.50/170.81 (define @t74 () (_ tptp.ap @t8)) % 170.50/170.81 (define @t75 () (_ @t74 @t24)) % 170.50/170.81 (define @t76 () (_ @t69 @t8)) % 170.50/170.81 (define @t77 () (not @t76)) % 170.50/170.81 (define @t78 () (not (forall @t32 (or @t77 @t72 (_ @t69 @t75))))) % 170.50/170.81 (define @t79 () (not (forall @t11 (or (not (_ tptp.var @t8)) @t76)))) % 170.50/170.81 (define @t80 () (forall (@list @t69 @t68) (or @t79 @t78 @t73 (_ @t69 @t68)))) % 170.50/170.81 (define @t81 () (@list @t53)) % 170.50/170.81 (define @t82 () (forall (@list @t2) (not (forall @t81 @t65)))) % 170.50/170.81 (define @t83 () (@var "Bound_variable_2910" tptp.term)) % 170.50/170.81 (define @t84 () (forall (@list @t2 @t53 @t83) (or @t50 @t46 @t23 @t65 (not (forall @t58 (or @t57 (_ @t53 (_ (_ tptp.sub @t83) @t55))))) (_ @t53 (_ tptp.lam @t83))))) % 170.50/170.81 (define @t85 () (_ (_ tptp.push @t8) @t16)) % 170.50/170.81 (define @t86 () (forall @t63 (= @t61 (_ @t69 (_ (_ tptp.sub @t59) @t85))))) % 170.50/170.81 (define @t87 () (not @t86)) % 170.50/170.81 (define @t88 () (forall (@list @t69 @t8 @t16) (not (forall @t81 @t87)))) % 170.50/170.81 (define @t89 () (_ tptp.comp tptp.sh)) % 170.50/170.81 (define @t90 () (@list @t8 @t16)) % 170.50/170.81 (define @t91 () (forall @t90 (= @t16 (_ @t89 @t85)))) % 170.50/170.81 (define @t92 () (@var "K" (-> tptp.term Bool))) % 170.50/170.81 (define @t93 () (forall (@list @t69 @t92 @t8 @t16 @t24) (or @t77 (_ @t92 (_ @t14 (_ @t54 @t16)))))) % 170.50/170.81 (define @t94 () (_ tptp.sub tptp.one)) % 170.50/170.81 (define @t95 () (forall @t90 (= @t8 (_ @t94 @t85)))) % 170.50/170.81 (define @t96 () (@var "Bound_variable_2605" tptp.term)) % 170.50/170.81 (define @t97 () (@var "Bound_variable_2603" tptp.term)) % 170.50/170.81 (define @t98 () (_ tptp.d2subst tptp.d_id)) % 170.50/170.81 (define @t99 () (_ tptp.d2term tptp.d_one)) % 170.50/170.81 (define @t100 () (@var "Bound_variable_3295" tptp.term)) % 170.50/170.81 (define @t101 () (forall (@list @t2 @t100) (or @t34 @t23 (_ (_ @t3 @t100) tptp.id)))) % 170.50/170.81 (define @t102 () (@var "Bound_variable_3232" tptp.term)) % 170.50/170.81 (define @t103 () (forall (@list @t2 @t102) (or @t23 (not (forall @t58 (or @t30 (_ (_ @t3 (_ (_ tptp.sub @t102) @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t102)) tptp.id)))) % 170.50/170.81 (define @t104 () (@list @t16)) % 170.50/170.81 (define @t105 () (forall @t104 (= @t16 (_ @t17 tptp.id)))) % 170.50/170.81 (define @t106 () (forall @t104 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 170.50/170.81 (define @t107 () (and @t106 @t105)) % 170.50/170.81 (define @t108 () (_ (_ tptp.push tptp.one) tptp.sh)) % 170.50/170.81 (define @t109 () (_ tptp.sub @t24)) % 170.50/170.81 (define @t110 () (forall @t58 (not (forall @t22 (not (= @t5 (_ @t109 @t108))))))) % 170.50/170.81 (define @t111 () (@var "Bound_variable_2342" tptp.subst)) % 170.50/170.81 (define @t112 () (@var "Bound_variable_2340" tptp.term)) % 170.50/170.81 (define @t113 () (forall (@list @t69 @t112 @t111) (or @t78 @t73 (not (forall @t58 (or (not (_ tptp.var @t24)) (_ @t69 (_ @t109 @t111))))) (_ @t69 (_ (_ tptp.sub @t112) @t111))))) % 170.50/170.81 (define @t114 () (forall @t58 (not (forall @t22 (not (forall @t90 (= (_ @t109 @t85) @t19))))))) % 170.50/170.81 (define @t115 () (@var "Bound_variable_3211" tptp.term)) % 170.50/170.81 (define @t116 () (forall (@list @t2 @t115) (or @t50 @t46 @t23 (not (forall @t58 (or @t30 (_ (_ @t3 (_ (_ tptp.sub @t115) @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t115)) tptp.id)))) % 170.50/170.81 (define @t117 () (@var "Bound_variable_3046" tptp.term)) % 170.50/170.81 (define @t118 () (_ tptp.sub @t117)) % 170.50/170.81 (define @t119 () (forall (@list @t2 @t117) (or @t23 (not (forall @t58 (or @t30 (_ (_ @t3 (_ @t118 @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t118 @t108))) tptp.id)))) % 170.50/170.81 (define @t120 () (= @t8 @t24)) % 170.50/170.81 (define @t121 () (forall @t32 (or (not (= @t70 (_ tptp.lam @t24))) @t120))) % 170.50/170.81 (define @t122 () (@var "Bound_variable_2551" tptp.term)) % 170.50/170.81 (define @t123 () (@var "Bound_variable_2549" tptp.subst)) % 170.50/170.81 (define @t124 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 170.50/170.81 (define @t125 () (forall (@list @t4 @t124 @t123 @t122) (or @t21 (not (forall @t20 (= (_ (_ tptp.sub (_ (_ @t124 @t16) @t8)) @t13) (_ (_ @t124 @t18) @t15)))) (not (= @t6 (_ tptp.lam (_ (_ @t124 tptp.sh) tptp.one)))) (= (_ (_ @t4 @t123) @t122) (_ (_ @t124 @t123) @t122))))) % 170.50/170.81 (define @t126 () (@var "D" tptp.term)) % 170.50/170.81 (define @t127 () (@var "C" tptp.term)) % 170.50/170.81 (define @t128 () (not (= (_ @t26 @t127) (_ (_ tptp.ap (_ @t109 tptp.id)) @t126)))) % 170.50/170.81 (define @t129 () (@list @t8 @t24 @t127 @t126)) % 170.50/170.81 (define @t130 () (forall @t129 (or @t128 @t120))) % 170.50/170.81 (define @t131 () (not (= (_ @t74 @t127) (_ (_ tptp.ap @t24) @t126)))) % 170.50/170.81 (define @t132 () (forall @t129 (or @t131 @t120))) % 170.50/170.81 (define @t133 () (= @t127 @t126)) % 170.50/170.81 (define @t134 () (forall @t129 (or @t128 @t133))) % 170.50/170.81 (define @t135 () (forall @t129 (or @t131 @t133))) % 170.50/170.81 (define @t136 () (@var "Bound_variable_2822" tptp.term)) % 170.50/170.81 (define @t137 () (@var "Bound_variable_2820" tptp.term)) % 170.50/170.81 (define @t138 () (_ (_ tptp.ap @t137) @t136)) % 170.50/170.81 (define @t139 () (_ @t53 @t138)) % 170.50/170.81 (define @t140 () (_ @t53 @t136)) % 170.50/170.81 (define @t141 () (not @t140)) % 170.50/170.81 (define @t142 () (_ @t53 @t137)) % 170.50/170.81 (define @t143 () (not @t142)) % 170.50/170.81 (define @t144 () (or @t50 @t46 @t34 @t65 @t143 @t141 @t139)) % 170.50/170.81 (define @t145 () (@list @t2 @t53 @t137 @t136)) % 170.50/170.81 (define @t146 () (forall @t145 @t144)) % 170.50/170.81 (define @t147 () (= tptp.hoasinduction_lem2v2 @t146)) % 170.50/170.81 (define @t148 () (@var "Bound_variable_2140" tptp.term)) % 170.50/170.81 (define @t149 () (forall (@list @t69 @t148) (or @t79 @t78 (not (forall @t11 (or @t77 @t71))) (_ @t69 @t148)))) % 170.50/170.81 (define @t150 () (forall (@list @t69 @t53 @t8 @t16) (or @t77 @t87 (_ @t53 tptp.one)))) % 170.50/170.81 (define @t151 () (@var "Bound_variable_3001" tptp.term)) % 170.50/170.81 (define @t152 () (@var "Bound_variable_2999" tptp.term)) % 170.50/170.81 (define @t153 () (forall (@list @t2 @t152 @t151) (or @t50 @t46 @t34 (not (_ (_ @t3 @t152) tptp.id)) (not (_ (_ @t3 @t151) tptp.id)) (_ (_ @t3 (_ (_ tptp.ap @t152) @t151)) tptp.id)))) % 170.50/170.81 (define @t154 () (@var "Bound_variable_3171" tptp.term)) % 170.50/170.81 (define @t155 () (_ tptp.sub @t154)) % 170.50/170.81 (define @t156 () (@var "Bound_variable_3094" tptp.subst)) % 170.50/170.81 (define @t157 () (@var "Bound_variable_3090" tptp.subst)) % 170.50/170.81 (define @t158 () (_ (_ tptp.comp @t157) @t156)) % 170.50/170.81 (define @t159 () (@var "Bound_variable_3092" tptp.term)) % 170.50/170.81 (define @t160 () (_ (_ tptp.sub @t159) @t156)) % 170.50/170.81 (define @t161 () (@var "Bound_variable_3149" tptp.term)) % 170.50/170.81 (define @t162 () (_ tptp.sub @t161)) % 170.50/170.81 (define @t163 () (@var "Bound_variable_3076" tptp.subst)) % 170.50/170.81 (define @t164 () (@var "Bound_variable_3072" tptp.subst)) % 170.50/170.81 (define @t165 () (@var "Bound_variable_3074" tptp.term)) % 170.50/170.81 (define @t166 () (@list @t2 @t53)) % 170.50/170.81 (define @t167 () (lambda @t166 @t64)) % 170.50/170.81 (define @t168 () (= tptp.hoasinduction_p_and_p_prime @t167)) % 170.50/170.81 (define @t169 () (_ (_ (_ (_ tptp.hoasap @t98) @t99) @t98) @t99)) % 170.50/170.81 (define @t170 () (_ (_ tptp.sub @t99) @t98)) % 170.50/170.81 (define @t171 () (_ (_ tptp.ap @t99) @t99)) % 170.50/170.81 (define @t172 () (@var "DS2" tptp.d_subst)) % 170.50/170.81 (define @t173 () (@var "DS1" tptp.d_subst)) % 170.50/170.81 (define @t174 () (@var "DS" tptp.d_subst)) % 170.50/170.81 (define @t175 () (@list @t174)) % 170.50/170.81 (define @t176 () (@var "S" tptp.subst)) % 170.50/170.81 (define @t177 () (@var "DT2" tptp.d_term)) % 170.50/170.81 (define @t178 () (@var "DT1" tptp.d_term)) % 170.50/170.81 (define @t179 () (@var "DT" tptp.d_term)) % 170.50/170.81 (define @t180 () (@list @t179)) % 170.50/170.81 (define @t181 () (forall @t180 (= @t179 tptp.d_one))) % 170.50/170.81 (define @t182 () (_ tptp.d2term @t179)) % 170.50/170.81 (define @t183 () (@var "T" tptp.term)) % 170.50/170.81 (define @t184 () (= @t183 @t182)) % 170.50/170.81 (define @t185 () (exists @t180 @t184)) % 170.50/170.81 (define @t186 () (@list @t183)) % 170.50/170.81 (define @t187 () (forall @t186 @t185)) % 170.50/170.81 (define @t188 () (_ @t53 @t75)) % 170.50/170.81 (define @t189 () (=> @t56 @t188)) % 170.50/170.81 (define @t190 () (_ @t53 @t8)) % 170.50/170.81 (define @t191 () (forall @t32 (=> @t190 @t189))) % 170.50/170.81 (define @t192 () (_ (_ tptp.hoasinduction_p_and_p_prime @t2) @t53)) % 170.50/170.81 (define @t193 () (=> @t192 @t191)) % 170.50/170.81 (define @t194 () (_ (_ (_ (_ tptp.hoasap tptp.id) @t8) tptp.id) @t24)) % 170.50/170.81 (define @t195 () (_ (_ @t3 @t194) tptp.id)) % 170.50/170.81 (define @t196 () (=> @t29 @t195)) % 170.50/170.81 (define @t197 () (forall @t32 (=> @t9 @t196))) % 170.50/170.81 (define @t198 () (=> @t197 @t193)) % 170.50/170.81 (define @t199 () (forall @t44 (=> @t41 @t38))) % 170.50/170.81 (define @t200 () (=> @t199 @t198)) % 170.50/170.81 (define @t201 () (forall @t44 (=> @t38 @t41))) % 170.50/170.81 (define @t202 () (=> @t201 @t200)) % 170.50/170.81 (define @t203 () (forall @t166 @t202)) % 170.50/170.81 (define @t204 () (= tptp.hoasinduction_lem2v2 @t203)) % 170.50/170.81 (define @t205 () (not @t204)) % 170.50/170.81 (define @t206 () (_ (@const 1 (-> (@ho-elim-sort (-> tptp.d_subst tptp.subst)) tptp.d_subst tptp.subst)) (@const 0 (@ho-elim-sort (-> tptp.d_subst tptp.subst))) tptp.d_id)) % 170.50/170.81 (define @t207 () (@const 2 (@ho-elim-sort (-> tptp.d_term tptp.term)))) % 170.50/170.81 (define @t208 () (@const 3 (-> (@ho-elim-sort (-> tptp.d_term tptp.term)) tptp.d_term tptp.term))) % 170.50/170.81 (define @t209 () (_ @t208 @t207 tptp.d_one)) % 170.50/170.81 (define @t210 () (@const 4 (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)))) % 170.50/170.81 (define @t211 () (@const 5 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term))))) % 170.50/170.81 (define @t212 () (@const 6 (-> (@ho-elim-sort (-> tptp.subst tptp.term)) tptp.subst tptp.term))) % 170.50/170.81 (define @t213 () (_ @t212 (_ @t211 @t210 @t209) @t206)) % 170.50/170.81 (define @t214 () (= @t209 @t213)) % 170.50/170.81 (define @t215 () (@var "y" (@ho-elim-sort (-> tptp.term tptp.term)))) % 170.50/170.81 (define @t216 () (@var "x" (@ho-elim-sort (-> tptp.term tptp.term)))) % 170.50/170.81 (define @t217 () (@var "z" tptp.term)) % 170.50/170.81 (define @t218 () (@const 7 (-> (@ho-elim-sort (-> tptp.term tptp.term)) tptp.term tptp.term))) % 170.50/170.81 (define @t219 () (@list @t217)) % 170.50/170.81 (define @t220 () (_ (@const 9 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.subst tptp.term tptp.term)))) (@const 8 (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term))) @t206)) % 170.50/170.81 (define @t221 () (@const 10 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term tptp.term))))) % 170.50/170.81 (define @t222 () (@const 11 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.term)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.term))))) % 170.50/170.81 (define @t223 () (_ @t222 (_ @t221 @t220 @t209) @t206)) % 170.50/170.81 (define @t224 () (@const 12 (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 170.50/170.81 (define @t225 () (@const 13 (-> (@ho-elim-sort (-> tptp.term tptp.term tptp.term)) tptp.term (@ho-elim-sort (-> tptp.term tptp.term))))) % 170.50/170.81 (define @t226 () (_ @t225 @t224 @t209)) % 170.50/170.81 (define @t227 () (_ @t208 @t207 @t179)) % 170.50/170.81 (define @t228 () (forall @t186 (not (forall @t180 (not (= @t183 @t227)))))) % 170.50/170.81 (define @t229 () (tptp.d2term @t179)) % 170.50/170.81 (define @t230 () (not @t184)) % 170.50/170.81 (define @t231 () (forall @t180 @t230)) % 170.50/170.81 (define @t232 () (not @t231)) % 170.50/170.81 (define @t233 () (forall @t219 (= (_ @t218 @t226 @t217) (_ @t218 @t223 @t217)))) % 170.50/170.81 (define @t234 () (@quantifiers_skolemize @t233 0)) % 170.50/170.81 (define @t235 () (not (= @t234 @t227))) % 170.50/170.81 (define @t236 () (forall @t180 @t235)) % 170.50/170.81 (define @t237 () (not @t236)) % 170.50/170.81 (define @t238 () (forall @t180 (not (= @t227 @t234)))) % 170.50/170.81 (define @t239 () (not @t238)) % 170.50/170.81 (define @t240 () (@list false)) % 170.50/170.81 (define @t241 () (@list @t228)) % 170.50/170.81 (define @t242 () (@quantifiers_skolemize @t238 0)) % 170.50/170.81 (define @t243 () (_ @t208 @t207 @t242)) % 170.50/170.81 (define @t244 () (= @t234 @t243)) % 170.50/170.81 (define @t245 () (= @t243 @t234)) % 170.50/170.81 (define @t246 () (not (not @t245))) % 170.50/170.81 (define @t247 () (@list true)) % 170.50/170.81 (define @t248 () (_ @t218 @t223 @t209)) % 170.50/170.81 (define @t249 () (_ @t225 @t224 @t213)) % 170.50/170.81 (define @t250 () (_ @t218 @t226 @t234)) % 170.50/170.81 (define @t251 () (= @t250 (_ @t218 @t223 @t234))) % 170.50/170.81 (define @t252 () (not @t251)) % 170.50/170.81 (define @t253 () (not @t233)) % 170.50/170.81 (define @t254 () (= @t226 @t223)) % 170.50/170.81 (define @t255 () (or @t253 @t254)) % 170.50/170.81 (define @t256 () (@list false false)) % 170.50/170.81 (define @t257 () (@var "y" (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 170.50/170.81 (define @t258 () (@var "x" (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 170.50/170.81 (define @t259 () (@var "z" tptp.term)) % 170.50/170.81 (define @t260 () (@list @t259)) % 170.50/170.81 (define @t261 () (@var "ii" tptp.term)) % 170.50/170.81 (define @t262 () (ite (= @t209 @t261) @t226 (_ @t225 @t224 @t261))) % 170.50/170.81 (define @t263 () (@var "v" (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 170.50/170.81 (define @t264 () (_ @t225 @t263 @t261)) % 170.50/170.81 (define @t265 () (@list @t261)) % 170.50/170.81 (define @t266 () (@list @t263)) % 170.50/170.81 (define @t267 () (forall @t266 (not (forall @t265 (= @t264 @t262))))) % 170.50/170.81 (define @t268 () (@quantifiers_skolemize @t267 0)) % 170.50/170.81 (define @t269 () (forall @t260 (= (_ @t225 @t224 @t259) (_ @t225 @t268 @t259)))) % 170.50/170.81 (define @t270 () (@quantifiers_skolemize @t269 0)) % 170.50/170.81 (define @t271 () (not (= @t270 @t227))) % 170.50/170.81 (define @t272 () (forall @t180 @t271)) % 170.50/170.81 (define @t273 () (not @t272)) % 170.50/170.81 (define @t274 () (forall @t180 (not (= @t227 @t270)))) % 170.50/170.81 (define @t275 () (not @t274)) % 170.50/170.81 (define @t276 () (@quantifiers_skolemize @t274 0)) % 170.50/170.81 (define @t277 () (_ @t208 @t207 @t276)) % 170.50/170.81 (define @t278 () (= @t270 @t277)) % 170.50/170.81 (define @t279 () (= @t277 @t270)) % 170.50/170.81 (define @t280 () (not (not @t279))) % 170.50/170.81 (define @t281 () (_ @t225 @t268 @t209)) % 170.50/170.81 (define @t282 () (@var "u" (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 170.50/170.81 (define @t283 () (@var "e" (@ho-elim-sort (-> tptp.term tptp.term)))) % 170.50/170.81 (define @t284 () (@var "i" tptp.term)) % 170.50/170.81 (define @t285 () (_ @t225 @t268 @t261)) % 170.50/170.81 (define @t286 () (forall @t265 (= @t262 @t285))) % 170.50/170.81 (define @t287 () (not @t267)) % 170.50/170.81 (define @t288 () (forall @t265 (= @t285 @t262))) % 170.50/170.81 (define @t289 () (not (not @t288))) % 170.50/170.81 (define @t290 () (= @t209 @t209)) % 170.50/170.81 (define @t291 () (= (ite @t290 @t226 @t226) @t281)) % 170.50/170.81 (define @t292 () (_ @t225 @t224 @t270)) % 170.50/170.81 (define @t293 () (= @t292 (_ @t225 @t268 @t270))) % 170.50/170.81 (define @t294 () (not @t293)) % 170.50/170.81 (define @t295 () (not @t269)) % 170.50/170.81 (define @t296 () (= @t224 @t268)) % 170.50/170.81 (define @t297 () (or @t295 @t296)) % 170.50/170.81 (define @t298 () (@var "BOUND_VARIABLE_9066" tptp.term)) % 170.50/170.81 (define @t299 () (@var "BOUND_VARIABLE_9064" tptp.term)) % 170.50/170.81 (define @t300 () (@var "BOUND_VARIABLE_10146" (@ho-elim-sort (-> tptp.term Bool)))) % 170.50/170.81 (define @t301 () (@const 14 (-> (@ho-elim-sort (-> tptp.term Bool)) tptp.term Bool))) % 170.50/170.81 (define @t302 () (_ @t301 @t300 (_ @t218 (_ @t225 @t224 @t299) @t298))) % 170.50/170.81 (define @t303 () (not (_ @t301 @t300 @t298))) % 170.50/170.81 (define @t304 () (not (_ @t301 @t300 @t299))) % 170.50/170.81 (define @t305 () (_ @t301 @t300 @t59)) % 170.50/170.81 (define @t306 () (@var "BOUND_VARIABLE_10157" (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool)))) % 170.50/170.81 (define @t307 () (@const 15 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.subst Bool))))) % 170.50/170.81 (define @t308 () (_ @t307 @t306 @t206)) % 170.50/170.81 (define @t309 () (@const 16 (-> (@ho-elim-sort (-> tptp.term tptp.subst Bool)) tptp.term (@ho-elim-sort (-> tptp.subst Bool))))) % 170.50/170.81 (define @t310 () (@const 17 (-> (@ho-elim-sort (-> tptp.subst Bool)) tptp.subst Bool))) % 170.50/170.81 (define @t311 () (_ @t310 (_ @t309 @t308 @t59) @t206)) % 170.50/170.81 (define @t312 () (not (forall @t63 (= @t311 @t305)))) % 170.50/170.81 (define @t313 () (_ @t218 (_ @t222 (_ @t221 @t220 @t8) @t206) @t24)) % 170.50/170.81 (define @t314 () (not (_ @t310 (_ @t309 @t308 @t24) @t206))) % 170.50/170.81 (define @t315 () (not (_ @t310 (_ @t309 @t308 @t8) @t206))) % 170.50/170.81 (define @t316 () (not (forall @t32 (or @t315 @t314 (_ @t310 (_ @t309 @t308 @t313) @t206))))) % 170.50/170.81 (define @t317 () (@const 18 (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)))) % 170.50/170.81 (define @t318 () (@const 19 (-> (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)) tptp.subst (@ho-elim-sort (-> tptp.subst tptp.subst))))) % 170.50/170.81 (define @t319 () (@const 20 (-> (@ho-elim-sort (-> tptp.subst tptp.subst)) tptp.subst tptp.subst))) % 170.50/170.81 (define @t320 () (_ @t319 (_ @t318 @t317 @t35) @t13)) % 170.50/170.81 (define @t321 () (_ @t310 (_ @t309 (_ @t307 @t306 @t16) @t8) @t320)) % 170.50/170.81 (define @t322 () (_ @t211 @t210 @t8)) % 170.50/170.81 (define @t323 () (_ @t212 @t322 @t35)) % 170.50/170.81 (define @t324 () (_ @t319 (_ @t318 @t317 @t16) @t35)) % 170.50/170.81 (define @t325 () (_ @t310 (_ @t309 (_ @t307 @t306 @t324) @t323) @t13)) % 170.50/170.81 (define @t326 () (not (forall @t44 (or (not @t325) @t321)))) % 170.50/170.81 (define @t327 () (not (forall @t44 (or (not @t321) @t325)))) % 170.50/170.81 (define @t328 () (@list @t306 @t300 @t299 @t298)) % 170.50/170.81 (define @t329 () (forall @t328 (or @t327 @t326 @t316 @t312 @t304 @t303 @t302))) % 170.50/170.81 (define @t330 () (@quantifiers_skolemize @t329 2)) % 170.50/170.81 (define @t331 () (not (= @t330 @t227))) % 170.50/170.81 (define @t332 () (forall @t180 @t331)) % 170.50/170.81 (define @t333 () (not @t332)) % 170.50/170.81 (define @t334 () (@list @t330)) % 170.50/170.81 (define @t335 () (forall @t180 (not (= @t227 @t330)))) % 170.50/170.81 (define @t336 () (not @t335)) % 170.50/170.81 (define @t337 () (@quantifiers_skolemize @t335 0)) % 170.50/170.81 (define @t338 () (_ @t208 @t207 @t337)) % 170.50/170.81 (define @t339 () (= @t330 @t338)) % 170.50/170.81 (define @t340 () (= @t338 @t330)) % 170.50/170.81 (define @t341 () (not (not @t340))) % 170.50/170.81 (define @t342 () (_ @t218 (_ @t225 @t224 (_ @t212 @t322 @t206)) @t24)) % 170.50/170.81 (define @t343 () (_ @t301 @t300 (_ @t218 (_ @t225 @t224 @t137) @t136))) % 170.50/170.81 (define @t344 () (not (_ @t301 @t300 @t136))) % 170.50/170.81 (define @t345 () (not (_ @t301 @t300 @t137))) % 170.50/170.81 (define @t346 () (not (forall @t32 (or @t315 @t314 (_ @t310 (_ @t309 @t308 @t342) @t206))))) % 170.50/170.81 (define @t347 () (@list @t306 @t300 @t137 @t136)) % 170.50/170.81 (define @t348 () (forall @t347 (or @t327 @t326 @t346 @t312 @t345 @t344 @t343))) % 170.50/170.81 (define @t349 () (@quantifiers_skolemize @t348 0)) % 170.50/170.81 (define @t350 () (_ @t307 @t349 @t206)) % 170.50/170.81 (define @t351 () (forall @t32 (or (not (_ @t310 (_ @t309 @t350 @t8) @t206)) (not (_ @t310 (_ @t309 @t350 @t24) @t206)) (_ @t310 (_ @t309 @t350 @t342) @t206)))) % 170.50/170.81 (define @t352 () (@quantifiers_skolemize @t348 3)) % 170.50/170.81 (define @t353 () (@quantifiers_skolemize @t348 2)) % 170.50/170.81 (define @t354 () (_ @t218 (_ @t225 @t224 @t353) @t352)) % 170.50/170.81 (define @t355 () (@quantifiers_skolemize @t348 1)) % 170.50/170.81 (define @t356 () (_ @t301 @t355 @t354)) % 170.50/170.81 (define @t357 () (_ @t301 @t355 @t352)) % 170.50/170.81 (define @t358 () (not @t357)) % 170.50/170.81 (define @t359 () (_ @t301 @t355 @t353)) % 170.50/170.81 (define @t360 () (not @t359)) % 170.50/170.81 (define @t361 () (forall @t63 (= (_ @t310 (_ @t309 @t350 @t59) @t206) (_ @t301 @t355 @t59)))) % 170.50/170.81 (define @t362 () (not @t361)) % 170.50/170.81 (define @t363 () (not @t351)) % 170.50/170.81 (define @t364 () (_ @t310 (_ @t309 (_ @t307 @t349 @t16) @t8) @t320)) % 170.50/170.81 (define @t365 () (_ @t310 (_ @t309 (_ @t307 @t349 @t324) @t323) @t13)) % 170.50/170.81 (define @t366 () (or (not (forall @t44 (or (not @t364) @t365))) (not (forall @t44 (or (not @t365) @t364))) @t363 @t362 @t360 @t358 @t356)) % 170.50/170.81 (define @t367 () (_ @t218 @t249 @t352)) % 170.50/170.81 (define @t368 () (_ @t309 @t350 @t367)) % 170.50/170.81 (define @t369 () (_ @t310 @t368 @t206)) % 170.50/170.81 (define @t370 () (_ @t310 (_ @t309 @t350 @t352) @t206)) % 170.50/170.81 (define @t371 () (not @t370)) % 170.50/170.81 (define @t372 () (_ @t309 @t350 @t209)) % 170.50/170.81 (define @t373 () (_ @t310 @t372 @t206)) % 170.50/170.81 (define @t374 () (not @t373)) % 170.50/170.81 (define @t375 () (or @t374 @t371 @t369)) % 170.50/170.81 (define @t376 () (_ @t310 (_ @t309 @t350 @t353) @t206)) % 170.50/170.81 (define @t377 () (= @t376 @t359)) % 170.50/170.81 (define @t378 () (@list @t353)) % 170.50/170.81 (define @t379 () (= @t370 @t357)) % 170.50/170.81 (define @t380 () (= @t359 @t376)) % 170.50/170.81 (define @t381 () (= @t357 @t370)) % 170.50/170.81 (define @t382 () (not (= @t353 @t227))) % 170.50/170.81 (define @t383 () (forall @t180 @t382)) % 170.50/170.81 (define @t384 () (not @t383)) % 170.50/170.81 (define @t385 () (forall @t180 (not (= @t227 @t353)))) % 170.50/170.81 (define @t386 () (not @t385)) % 170.50/170.81 (define @t387 () (@quantifiers_skolemize @t385 0)) % 170.50/170.81 (define @t388 () (_ @t208 @t207 @t387)) % 170.50/170.81 (define @t389 () (= @t353 @t388)) % 170.50/170.81 (define @t390 () (= @t388 @t353)) % 170.50/170.81 (define @t391 () (not (not @t390))) % 170.50/170.81 (define @t392 () (= tptp.d_one @t387)) % 170.50/170.81 (define @t393 () (and @t376 @t389 @t392)) % 170.50/170.81 (define @t394 () (not @t392)) % 170.50/170.81 (define @t395 () (not @t389)) % 170.50/170.81 (define @t396 () (_ @t310 (_ @t309 @t350 @t354) @t206)) % 170.50/170.81 (define @t397 () (= @t396 @t356)) % 170.50/170.81 (define @t398 () (= @t356 @t396)) % 170.50/170.81 (define @t399 () (not @t396)) % 170.50/170.81 (define @t400 () (not @t369)) % 170.50/170.81 (define @t401 () (not @t214)) % 170.50/170.81 (define @t402 () (= true false)) % 170.50/170.81 (define @t403 () (and @t399 @t389 @t392 @t214 @t369)) % 170.50/170.81 (define @t404 () (not @t366)) % 170.50/170.81 (define @t405 () (not @t348)) % 170.50/170.81 (define @t406 () (forall @t63 (= @t305 @t311))) % 170.50/170.81 (define @t407 () (not @t406)) % 170.50/170.81 (define @t408 () (or @t327 @t326 @t346 @t407 @t345 @t344 @t343)) % 170.50/170.81 (define @t409 () (forall @t347 @t408)) % 170.50/170.81 (define @t410 () (or @t327 @t326 @t316 @t407 @t304 @t303 @t302)) % 170.50/170.81 (define @t411 () (forall @t328 @t410)) % 170.50/170.81 (define @t412 () (not (= @t409 @t411))) % 170.50/170.81 (define @t413 () (_ @t53 (tptp.ap @t299 @t298))) % 170.50/170.81 (define @t414 () (not (_ @t53 @t298))) % 170.50/170.81 (define @t415 () (not (_ @t53 @t299))) % 170.50/170.81 (define @t416 () (tptp.d2subst tptp.d_id)) % 170.50/170.81 (define @t417 () (_ @t53 @t59)) % 170.50/170.81 (define @t418 () (forall @t63 (= @t417 (_ @t2 @t416 @t59 @t416)))) % 170.50/170.81 (define @t419 () (not @t418)) % 170.50/170.81 (define @t420 () (not (_ @t2 @t416 @t24 @t416))) % 170.50/170.81 (define @t421 () (not (_ @t2 @t416 @t8 @t416))) % 170.50/170.81 (define @t422 () (tptp.comp @t35 @t13)) % 170.50/170.81 (define @t423 () (_ @t2 @t16 @t8 @t422)) % 170.50/170.81 (define @t424 () (tptp.sub @t8 @t35)) % 170.50/170.81 (define @t425 () (tptp.comp @t16 @t35)) % 170.50/170.81 (define @t426 () (_ @t2 @t425 @t424 @t13)) % 170.50/170.81 (define @t427 () (forall @t44 (or (not @t426) @t423))) % 170.50/170.81 (define @t428 () (not @t427)) % 170.50/170.81 (define @t429 () (forall @t44 (or (not @t423) @t426))) % 170.50/170.81 (define @t430 () (not @t429)) % 170.50/170.81 (define @t431 () (@list @t2 @t53 @t299 @t298)) % 170.50/170.81 (define @t432 () (tptp.ap @t137 @t136)) % 170.50/170.81 (define @t433 () (_ @t53 @t432)) % 170.50/170.81 (define @t434 () (_ @t53 @t136)) % 170.50/170.81 (define @t435 () (not @t434)) % 170.50/170.81 (define @t436 () (_ @t53 @t137)) % 170.50/170.81 (define @t437 () (not @t436)) % 170.50/170.81 (define @t438 () (forall @t145 (or @t430 @t428 (not (forall @t32 (or @t421 @t420 (_ @t2 @t416 (tptp.ap (tptp.sub @t8 @t416) @t24) @t416)))) @t419 @t437 @t435 @t433))) % 170.50/170.81 (define @t439 () (_ (lambda @t166 @t418) @t2 @t53)) % 170.50/170.81 (define @t440 () (not @t439)) % 170.50/170.81 (define @t441 () (tptp.hoasap @t98 @t8 @t98 @t24)) % 170.50/170.81 (define @t442 () (_ @t2 @t98 @t441 @t98)) % 170.50/170.81 (define @t443 () (_ @t2 @t98 @t24 @t98)) % 170.50/170.81 (define @t444 () (not @t443)) % 170.50/170.81 (define @t445 () (_ @t2 @t98 @t8 @t98)) % 170.50/170.81 (define @t446 () (not @t445)) % 170.50/170.81 (define @t447 () (or @t446 @t444 @t442)) % 170.50/170.81 (define @t448 () (forall @t32 @t447)) % 170.50/170.81 (define @t449 () (not @t448)) % 170.50/170.81 (define @t450 () (or @t430 @t428 @t449 @t440 @t415 @t414 @t413)) % 170.50/170.81 (define @t451 () (forall @t431 @t450)) % 170.50/170.81 (define @t452 () (= @t438 @t451)) % 170.50/170.81 (define @t453 () (_ @t2 @t98 @t59 @t98)) % 170.50/170.81 (define @t454 () (= @t417 @t453)) % 170.50/170.81 (define @t455 () (forall @t63 @t454)) % 170.50/170.81 (define @t456 () (lambda @t166 @t455)) % 170.50/170.81 (define @t457 () (_ @t2 tptp.id @t59 tptp.id)) % 170.50/170.81 (define @t458 () (= @t417 @t457)) % 170.50/170.81 (define @t459 () (forall @t63 @t458)) % 170.50/170.81 (define @t460 () (lambda @t166 @t459)) % 170.50/170.81 (define @t461 () (tptp.hoasinduction_p_and_p_prime @t2 @t53)) % 170.50/170.81 (define @t462 () (not @t461)) % 170.50/170.81 (define @t463 () (tptp.hoasap tptp.id @t8 tptp.id @t24)) % 170.50/170.81 (define @t464 () (_ @t2 tptp.id @t463 tptp.id)) % 170.50/170.81 (define @t465 () (_ @t2 tptp.id @t24 tptp.id)) % 170.50/170.81 (define @t466 () (not @t465)) % 170.50/170.81 (define @t467 () (_ @t2 tptp.id @t8 tptp.id)) % 170.50/170.81 (define @t468 () (not @t467)) % 170.50/170.81 (define @t469 () (or @t468 @t466 @t464)) % 170.50/170.81 (define @t470 () (forall @t32 @t469)) % 170.50/170.81 (define @t471 () (not @t470)) % 170.50/170.81 (define @t472 () (or @t430 @t428 @t471 @t462 @t415 @t414 @t413)) % 170.50/170.81 (define @t473 () (forall @t431 @t472)) % 170.50/170.81 (define @t474 () (not @t455)) % 170.50/170.81 (define @t475 () (tptp.sub @t8 @t98)) % 170.50/170.81 (define @t476 () (tptp.ap @t475 @t24)) % 170.50/170.81 (define @t477 () (_ @t2 @t98 @t476 @t98)) % 170.50/170.81 (define @t478 () (or @t446 @t444 @t477)) % 170.50/170.81 (define @t479 () (forall @t32 @t478)) % 170.50/170.81 (define @t480 () (not @t479)) % 170.50/170.81 (define @t481 () (or @t430 @t428 @t480 @t474 @t437 @t435 @t433)) % 170.50/170.81 (define @t482 () (forall @t145 @t481)) % 170.50/170.81 (define @t483 () (not @t459)) % 170.50/170.81 (define @t484 () (tptp.sub @t8 tptp.id)) % 170.50/170.81 (define @t485 () (tptp.ap @t484 @t24)) % 170.50/170.81 (define @t486 () (_ @t2 tptp.id @t485 tptp.id)) % 170.50/170.81 (define @t487 () (or @t468 @t466 @t486)) % 170.50/170.81 (define @t488 () (forall @t32 @t487)) % 170.50/170.81 (define @t489 () (not @t488)) % 170.50/170.81 (define @t490 () (or @t430 @t428 @t489 @t483 @t437 @t435 @t433)) % 170.50/170.81 (define @t491 () (forall @t145 @t490)) % 170.50/170.81 (define @t492 () (or @t430 @t428 @t489 @t483 @t143 @t141 @t139)) % 170.50/170.81 (define @t493 () (= tptp.hoasinduction_lem2v2 @t473)) % 170.50/170.81 (define @t494 () (or @t415 @t414 @t413)) % 170.50/170.81 (define @t495 () (or @t430 @t428 @t471 @t462 @t494)) % 170.50/170.81 (define @t496 () (forall @t431 @t495)) % 170.50/170.81 (define @t497 () (@list @t299 @t298)) % 170.50/170.81 (define @t498 () (forall @t497 @t495)) % 170.50/170.81 (define @t499 () (forall @t497 @t494)) % 170.50/170.81 (define @t500 () (or @t430 @t428 @t471 @t462 @t499)) % 170.50/170.81 (define @t501 () (tptp.ap @t8 @t24)) % 170.50/170.81 (define @t502 () (_ @t53 @t501)) % 170.50/170.81 (define @t503 () (_ @t53 @t24)) % 170.50/170.81 (define @t504 () (_ @t53 @t8)) % 170.50/170.81 (define @t505 () (forall @t32 (or (not @t504) (not @t503) @t502))) % 170.50/170.81 (define @t506 () (not @t192)) % 170.50/170.81 (define @t507 () (or @t430 @t428 @t471 @t506 @t505)) % 170.50/170.81 (define @t508 () (or @t428 @t471 @t506 @t505)) % 170.50/170.81 (define @t509 () (or @t471 @t506 @t505)) % 170.50/170.81 (define @t510 () (=> @t192 @t505)) % 170.50/170.81 (define @t511 () (=> @t470 @t510)) % 170.50/170.81 (define @t512 () (=> @t427 @t511)) % 170.50/170.81 (define @t513 () (not @t190)) % 170.50/170.81 (define @t514 () (or @t513 @t57 @t188)) % 170.50/170.81 (define @t515 () (or @t10 @t30 @t195)) % 170.50/170.81 (define @t516 () (not @t329)) % 170.50/170.81 (define @t517 () (@quantifiers_skolemize @t329 3)) % 170.50/170.81 (define @t518 () (_ @t218 (_ @t225 @t224 @t330) @t517)) % 170.50/170.81 (define @t519 () (@quantifiers_skolemize @t329 1)) % 170.50/170.81 (define @t520 () (_ @t301 @t519 @t518)) % 170.50/170.81 (define @t521 () (_ @t301 @t519 @t517)) % 170.50/170.81 (define @t522 () (not @t521)) % 170.50/170.81 (define @t523 () (_ @t301 @t519 @t330)) % 170.50/170.81 (define @t524 () (not @t523)) % 170.50/170.81 (define @t525 () (@quantifiers_skolemize @t329 0)) % 170.50/170.81 (define @t526 () (_ @t307 @t525 @t206)) % 170.50/170.81 (define @t527 () (forall @t63 (= (_ @t310 (_ @t309 @t526 @t59) @t206) (_ @t301 @t519 @t59)))) % 170.50/170.81 (define @t528 () (not @t527)) % 170.50/170.81 (define @t529 () (forall @t32 (or (not (_ @t310 (_ @t309 @t526 @t8) @t206)) (not (_ @t310 (_ @t309 @t526 @t24) @t206)) (_ @t310 (_ @t309 @t526 @t313) @t206)))) % 170.50/170.81 (define @t530 () (not @t529)) % 170.50/170.81 (define @t531 () (_ @t310 (_ @t309 (_ @t307 @t525 @t16) @t8) @t320)) % 170.50/170.81 (define @t532 () (_ @t310 (_ @t309 (_ @t307 @t525 @t324) @t323) @t13)) % 170.50/170.81 (define @t533 () (or (not (forall @t44 (or (not @t531) @t532))) (not (forall @t44 (or (not @t532) @t531))) @t530 @t528 @t524 @t522 @t520)) % 170.50/170.81 (define @t534 () (not @t533)) % 170.50/170.81 (define @t535 () (@list @t533)) % 170.50/170.81 (define @t536 () (_ @t218 @t223 @t517)) % 170.50/170.81 (define @t537 () (_ @t309 @t526 @t536)) % 170.50/170.81 (define @t538 () (_ @t310 @t537 @t206)) % 170.50/170.81 (define @t539 () (_ @t310 (_ @t309 @t526 @t517) @t206)) % 170.50/170.81 (define @t540 () (not @t539)) % 170.50/170.81 (define @t541 () (_ @t309 @t526 @t209)) % 170.50/170.81 (define @t542 () (_ @t310 @t541 @t206)) % 170.50/170.81 (define @t543 () (not @t542)) % 170.50/170.81 (define @t544 () (or @t543 @t540 @t538)) % 170.50/170.81 (define @t545 () (= @t539 @t521)) % 170.50/170.81 (define @t546 () (= @t521 @t539)) % 170.50/170.81 (define @t547 () (@list @t527)) % 170.50/170.81 (define @t548 () (_ @t310 (_ @t309 @t526 @t330) @t206)) % 170.50/170.81 (define @t549 () (= @t548 @t523)) % 170.50/170.81 (define @t550 () (= @t523 @t548)) % 170.50/170.81 (define @t551 () (= tptp.d_one @t337)) % 170.50/170.81 (define @t552 () (and @t548 @t339 @t551)) % 170.50/170.81 (define @t553 () (not @t551)) % 170.50/170.81 (define @t554 () (not @t339)) % 170.50/170.81 (define @t555 () (@list false false false)) % 170.50/170.81 (define @t556 () (_ @t310 (_ @t309 @t526 @t518) @t206)) % 170.50/170.81 (define @t557 () (= @t556 @t520)) % 170.50/170.81 (define @t558 () (= @t520 @t556)) % 170.50/170.81 (define @t559 () (not @t556)) % 170.50/170.81 (define @t560 () (not @t538)) % 170.50/170.81 (define @t561 () (not @t296)) % 170.50/170.81 (define @t562 () (not @t254)) % 170.50/170.81 (define @t563 () (and @t559 @t296 @t339 @t551 @t214 @t254 @t538)) % 170.50/170.81 (assume @p1 (and @t187 @t181 (forall (@list @t178 @t177) (=> (= (_ tptp.d2term @t178) (_ tptp.d2term @t177)) (= @t178 @t177))) (forall (@list @t176) (exists @t175 (= @t176 (_ tptp.d2subst @t174)))) (forall @t175 (= @t174 tptp.d_id)) (forall (@list @t173 @t172) (=> (= (_ tptp.d2subst @t173) (_ tptp.d2subst @t172)) (= @t173 @t172))) (= tptp.one @t99) (= @t171 @t99) (= (_ tptp.lam @t99) @t99) (= @t170 @t99) (= tptp.id @t98) (= tptp.sh @t98) (= (_ (_ tptp.push @t99) @t98) @t98) (= (_ (_ tptp.comp @t98) @t98) @t98) (= @t169 @t99) (= tptp.hoaslam (lambda (@list (@var "Bound_variable_4913" tptp.subst) (@var "Bound_variable_4915" (-> tptp.subst tptp.term tptp.term))) @t99)) @t168 (= tptp.pushprop_p_and_p_prime (lambda (@list @t8 @t16 @t69 @t53) @t86)) (not (_ tptp.var @t99)) (= tptp.pushprop_lem1v2 @t150) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t32 (or (not (= (_ @t14 tptp.sh) (_ @t109 tptp.sh))) @t120))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t113) (= tptp.hoasinduction_lem3v2_f @t114) tptp.axvarshift (= tptp.hoasapinj2 @t134) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t130) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t95 (=> @t91 (=> @t105 (=> @t149 @t113))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t114) (= tptp.hoasinduction_lthm (=> @t80 (=> @t153 (=> @t116 @t51)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t82 (=> @t80 (=> @t67 (=> @t66 @t101))))) (= tptp.hoaslaminj @t125) (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t154) (or (not (forall (@list @t4 @t161) (or @t12 @t7 (not (forall (@list @t164 @t165 @t163) (= (_ (_ tptp.sub (_ (_ @t4 @t164) @t165)) @t163) (_ (_ tptp.sub (_ @t162 (_ (_ tptp.push @t165) @t164))) @t163)))) (not (forall (@list @t157 @t159 @t156) (= (_ (_ @t4 @t158) @t160) (_ @t162 (_ (_ tptp.push @t160) @t158)))))))) (not (forall @t58 (or @t30 (_ (_ @t3 (_ @t155 @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t155 @t108))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t119) (= tptp.hoasinduction_lem3 @t116) (= tptp.hoasinduction_lem2 @t153) (= tptp.termmset_lthm (=> @t67 @t67)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t95 @t150)) tptp.hoasapnotvar (= tptp.hoasinduction_lem0 @t82) (= tptp.hoasinduction @t51) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t110) tptp.ulamvarind (= tptp.induction @t149) (= tptp.hoasinduction_lem3a_lthm (=> @t67 (=> @t119 @t103))) tptp.termmset_gthm (= tptp.hoasinduction_lem3aa @t119) tptp.pushprop_lem1v2_gthm tptp.hoaslamnotap_gthm tptp.hoaslamnotvar_gthm tptp.hoasinduction_lem3b_gthm tptp.pushprop_lem2v2 tptp.hoasinduction_lem3a_gthm tptp.axclos tptp.axassoc @t147 tptp.pushprop_lthm (= tptp.apinj2 @t135) (= tptp.apinj1 @t132) (= tptp.hoasapinj2_lthm (=> @t135 @t134)) (= tptp.hoasinduction_lem3v2a @t66) (= tptp.hoasapinj1_lthm (=> @t67 (=> @t132 @t130))) (= tptp.hoaslaminj_lthm (=> @t95 (=> @t91 (=> @t121 @t125)))) (= tptp.axvarcons @t95) (= tptp.axscons (forall @t104 (= @t16 (_ (_ tptp.push (_ @t94 @t16)) (_ @t89 @t16))))) tptp.hoasinduction_lem2v2_gthm (= tptp.axidr @t105) (= tptp.pushprop_lem1 @t93) (= tptp.laminj @t121) (= tptp.hoasinduction_lem3_lthm (=> @t67 (=> @t119 @t116))) (= tptp.pushprop_lem0 @t88) tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t114 (=> @t67 @t66))) tptp.hoasinduction_lem2_lthm tptp.hoasapinj2_gthm tptp.hoasinduction_lem1_lthm (not tptp.lamnotap) tptp.hoasapinj1_gthm tptp.hoaslamnotvar (= tptp.axidl @t106) tptp.hoaslaminj_gthm (= tptp.induction2_lthm (=> @t67 (=> @t113 @t80))) (= tptp.hoasinduction_lem0_lthm @t82) (= tptp.substmonoid_lthm (=> @t106 (=> @t105 @t107))) tptp.pushprop tptp.hoasinduction_lem3_gthm tptp.hoasinduction_lem2_gthm (= tptp.hoasinduction_lem3b @t110) (= tptp.substmonoid @t107) tptp.lamnotvar (= tptp.hoasinduction_lem3a @t103) tptp.hoasinduction_lem1_gthm (= tptp.hoasinduction_no_psi_cond @t101) tptp.induction2_gthm tptp.pushprop_lem2v2_lthm (not (_ (_ (_ tptp.hoasvar @t98) @t99) @t98)) (= tptp.hoaslamnotap (forall (@list @t4 @t97 @t96) (or @t21 (not (= @t6 (_ (_ tptp.ap (_ (_ tptp.sub @t97) tptp.id)) @t96)))))) tptp.substmonoid_gthm tptp.ulamvarsh (= tptp.induction2 @t80) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t95 (=> @t91 @t93))) (= tptp.hoasinduction_lem3v2 @t84) (= tptp.axshiftcons @t91) (= tptp.termmset @t67) (= tptp.pushprop_lem0_lthm @t88) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t67 @t84)) (= tptp.axvarid @t67) (= tptp.hoasinduction_lthm_3 (=> @t82 (=> @t80 (=> @t67 (=> @t66 @t51))))))) % 170.50/170.81 (assume @p2 @t205) % 170.50/170.81 (assume @p3 true) % 170.50/170.81 ; WARNING: add trust step for TRUST % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM % 170.50/170.81 (step @p4 :rule trust :premises () :args ((= (= @t99 @t170) @t214))) % 170.50/170.81 (step @p5 :rule eq-symm :args (@t170 @t99)) % 170.50/170.81 (step @p6 :rule trans :premises (@p5 @p4)) % 170.50/170.81 (step @p7 :rule and_elim :premises (@p1) :args (9)) % 170.50/170.81 (step @p8 :rule eq_resolve :premises (@p7 @p6)) % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.50/170.81 (step @p9 :rule trust :premises () :args ((forall (@list @t216 @t215) (or (not (forall @t219 (= (_ @t218 @t216 @t217) (_ @t218 @t215 @t217)))) (= @t216 @t215))))) % 170.50/170.81 (step @p10 :rule instantiate :premises (@p9) :args ((@list @t226 @t223))) % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM % 170.50/170.81 (step @p11 :rule trust :premises () :args ((= (forall @t186 (not (forall @t180 (not (= @t183 @t229))))) @t228))) % 170.50/170.81 (step @p12 :rule refl :args (@t229)) % 170.50/170.81 (step @p13 :rule refl :args (@t182)) % 170.50/170.81 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t182 @t229))) % 170.50/170.81 (step @p15 :rule symm :premises (@p14)) % 170.50/170.81 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 170.50/170.81 (step @p17 :rule refl :args (@t183)) % 170.50/170.81 (step @p18 :rule cong :premises (@p17 @p16) :args (@t184)) % 170.50/170.81 (step @p19 :rule cong :premises (@p18) :args (@t230)) % 170.50/170.81 (step @p20 :rule cong :premises (@p19) :args (@t231)) % 170.50/170.81 (step @p21 :rule cong :premises (@p20) :args (@t232)) % 170.50/170.81 (step @p22 :rule exists-elim :args ((= @t185 @t232))) % 170.50/170.81 (step @p23 :rule trans :premises (@p22 @p21)) % 170.50/170.81 (step @p24 :rule cong :premises (@p23) :args (@t187)) % 170.50/170.81 (step @p25 :rule trans :premises (@p24 @p11)) % 170.50/170.81 (step @p26 :rule and_elim :premises (@p1) :args (0)) % 170.50/170.81 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 170.50/170.81 (step @p28 :rule eq-symm :args (@t234 @t227)) % 170.50/170.81 (step @p29 :rule cong :premises (@p28) :args (@t235)) % 170.50/170.81 (step @p30 :rule cong :premises (@p29) :args (@t236)) % 170.50/170.81 (step @p31 :rule cong :premises (@p30) :args (@t237)) % 170.50/170.81 (step @p32 :rule refl :args (@t228)) % 170.50/170.81 (step @p33 :rule cong :premises (@p32 @p31) :args ((=> @t228 @t237))) % 170.50/170.81 (assume-push @p959 @t228) % 170.50/170.81 (step @p35 :rule instantiate :premises (@p27) :args ((@list @t234))) % 170.50/170.81 (step-pop @p960 :rule scope :premises (@p35)) % 170.50/170.81 (step @p36 :rule process_scope :premises (@p960) :args (@t237)) % 170.50/170.81 (step @p38 :rule eq_resolve :premises (@p36 @p33)) % 170.50/170.81 (step @p39 :rule implies_elim :premises (@p38)) % 170.50/170.81 (step @p40 :rule chain_m_resolution :premises (@p39 @p27) :args (@t239 @t240 @t241)) % 170.50/170.81 (step @p41 :rule refl :args (@t244)) % 170.50/170.81 (step @p42 :rule bool-double-not-elim :args (@t238)) % 170.50/170.81 (step @p43 :rule nary_cong :premises (@p42 @p41) :args ((or (not @t239) @t244))) % 170.50/170.81 (step @p44 :rule eq-symm :args (@t243 @t234)) % 170.50/170.81 (step @p45 :rule bool-double-not-elim :args (@t245)) % 170.50/170.81 (step @p46 :rule trans :premises (@p45 @p44)) % 170.50/170.81 (step @p47 :rule refl :args (@t239)) % 170.50/170.81 (step @p48 :rule cong :premises (@p47 @p46) :args ((=> @t239 @t246))) % 170.50/170.81 (assume-push @p961 @t239) % 170.50/170.81 (step @p50 :rule skolemize :premises (@p40)) % 170.50/170.81 (step-pop @p962 :rule scope :premises (@p50)) % 170.50/170.81 (step @p51 :rule process_scope :premises (@p962) :args (@t246)) % 170.50/170.81 (step @p53 :rule eq_resolve :premises (@p51 @p48)) % 170.50/170.81 (step @p54 :rule implies_elim :premises (@p53)) % 170.50/170.81 (step @p55 :rule eq_resolve :premises (@p54 @p43)) % 170.50/170.81 (step @p56 :rule chain_m_resolution :premises (@p55 @p40) :args (@t244 @t247 (@list @t238))) % 170.50/170.81 (step @p57 :rule symm :premises (@p56)) % 170.50/170.81 (step @p58 :rule eq-symm :args (@t179 tptp.d_one)) % 170.50/170.81 (step @p59 :rule cong :premises (@p58) :args (@t181)) % 170.50/170.81 (step @p60 :rule and_elim :premises (@p1) :args (1)) % 170.50/170.81 (step @p61 :rule eq_resolve :premises (@p60 @p59)) % 170.50/170.81 (step @p62 :rule instantiate :premises (@p61) :args ((@list @t242))) % 170.50/170.81 (step @p63 :rule refl :args (@t207)) % 170.50/170.81 (step @p64 :rule cong :premises (@p63 @p62) :args (@t209)) % 170.50/170.81 (step @p65 :rule trans :premises (@p64 @p57)) % 170.50/170.81 (step @p66 :rule refl :args (@t223)) % 170.50/170.81 (step @p67 :rule cong :premises (@p66 @p65) :args (@t248)) % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM % 170.50/170.81 (step @p68 :rule trust :premises () :args ((= (= @t99 @t169) (= @t209 @t248)))) % 170.50/170.81 (step @p69 :rule eq-symm :args (@t169 @t99)) % 170.50/170.81 (step @p70 :rule trans :premises (@p69 @p68)) % 170.50/170.81 (step @p71 :rule and_elim :premises (@p1) :args (14)) % 170.50/170.81 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM % 170.50/170.81 (step @p73 :rule trust :premises () :args ((= (= @t99 @t171) (= @t209 (_ @t218 @t226 @t209))))) % 170.50/170.81 (step @p74 :rule eq-symm :args (@t171 @t99)) % 170.50/170.81 (step @p75 :rule trans :premises (@p74 @p73)) % 170.50/170.81 (step @p76 :rule and_elim :premises (@p1) :args (7)) % 170.50/170.81 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 170.50/170.81 (step @p78 :rule symm :premises (@p77)) % 170.50/170.81 (step @p79 :rule refl :args (@t209)) % 170.50/170.81 (step @p80 :rule symm :premises (@p8)) % 170.50/170.81 (step @p81 :rule refl :args (@t224)) % 170.50/170.81 (step @p82 :rule cong :premises (@p81 @p80) :args (@t249)) % 170.50/170.81 (step @p83 :rule cong :premises (@p82 @p79) :args ((_ @t218 @t249 @t209))) % 170.50/170.81 (step @p84 :rule symm :premises (@p65)) % 170.50/170.81 (step @p85 :rule symm :premises (@p82)) % 170.50/170.81 (step @p86 :rule cong :premises (@p85 @p84) :args (@t250)) % 170.50/170.81 (step @p87 :rule trans :premises (@p86 @p83 @p78 @p72 @p67)) % 170.50/170.81 (step @p88 :rule refl :args (@t252)) % 170.50/170.81 (step @p89 :rule bool-double-not-elim :args (@t233)) % 170.50/170.81 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or (not @t253) @t252))) % 170.50/170.81 (assume-push @p963 @t253) % 170.50/170.81 (step @p92 :rule skolemize :premises (@p963)) % 170.50/170.81 (step-pop @p964 :rule scope :premises (@p92)) % 170.50/170.81 (step @p93 :rule process_scope :premises (@p964) :args (@t252)) % 170.50/170.81 (step @p95 :rule implies_elim :premises (@p93)) % 170.50/170.81 (step @p96 :rule eq_resolve :premises (@p95 @p90)) % 170.50/170.81 (step @p97 :rule chain_m_resolution :premises (@p96 @p87) :args (@t233 @t240 (@list @t251))) % 170.50/170.81 (step @p98 :rule cnf_or_pos :args (@t255)) % 170.50/170.81 (step @p99 :rule reordering :premises (@p98) :args ((or @t253 @t254 (not @t255)))) % 170.50/170.81 (step @p100 :rule chain_m_resolution :premises (@p99 @p97 @p10) :args (@t254 @t256 (@list @t233 @t255))) % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.50/170.81 (step @p101 :rule trust :premises () :args ((forall (@list @t258 @t257) (or (not (forall @t260 (= (_ @t225 @t258 @t259) (_ @t225 @t257 @t259)))) (= @t258 @t257))))) % 170.50/170.81 (step @p102 :rule instantiate :premises (@p101) :args ((@list @t224 @t268))) % 170.50/170.81 (step @p103 :rule eq-symm :args (@t270 @t227)) % 170.50/170.81 (step @p104 :rule cong :premises (@p103) :args (@t271)) % 170.50/170.81 (step @p105 :rule cong :premises (@p104) :args (@t272)) % 170.50/170.81 (step @p106 :rule cong :premises (@p105) :args (@t273)) % 170.50/170.81 (step @p107 :rule cong :premises (@p32 @p106) :args ((=> @t228 @t273))) % 170.50/170.81 (assume-push @p965 @t228) % 170.50/170.81 (step @p109 :rule instantiate :premises (@p27) :args ((@list @t270))) % 170.50/170.81 (step-pop @p966 :rule scope :premises (@p109)) % 170.50/170.81 (step @p110 :rule process_scope :premises (@p966) :args (@t273)) % 170.50/170.81 (step @p112 :rule eq_resolve :premises (@p110 @p107)) % 170.50/170.81 (step @p113 :rule implies_elim :premises (@p112)) % 170.50/170.81 (step @p114 :rule chain_m_resolution :premises (@p113 @p27) :args (@t275 @t240 @t241)) % 170.50/170.81 (step @p115 :rule refl :args (@t278)) % 170.50/170.81 (step @p116 :rule bool-double-not-elim :args (@t274)) % 170.50/170.81 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or (not @t275) @t278))) % 170.50/170.81 (step @p118 :rule eq-symm :args (@t277 @t270)) % 170.50/170.81 (step @p119 :rule bool-double-not-elim :args (@t279)) % 170.50/170.81 (step @p120 :rule trans :premises (@p119 @p118)) % 170.50/170.81 (step @p121 :rule refl :args (@t275)) % 170.50/170.81 (step @p122 :rule cong :premises (@p121 @p120) :args ((=> @t275 @t280))) % 170.50/170.81 (assume-push @p967 @t275) % 170.50/170.81 (step @p124 :rule skolemize :premises (@p114)) % 170.50/170.81 (step-pop @p968 :rule scope :premises (@p124)) % 170.50/170.81 (step @p125 :rule process_scope :premises (@p968) :args (@t280)) % 170.50/170.81 (step @p127 :rule eq_resolve :premises (@p125 @p122)) % 170.50/170.81 (step @p128 :rule implies_elim :premises (@p127)) % 170.50/170.81 (step @p129 :rule eq_resolve :premises (@p128 @p117)) % 170.50/170.81 (step @p130 :rule chain_m_resolution :premises (@p129 @p114) :args (@t278 @t247 (@list @t274))) % 170.50/170.81 (step @p131 :rule symm :premises (@p130)) % 170.50/170.81 (step @p132 :rule instantiate :premises (@p61) :args ((@list @t276))) % 170.50/170.81 (step @p133 :rule cong :premises (@p63 @p132) :args (@t209)) % 170.50/170.81 (step @p134 :rule trans :premises (@p133 @p131)) % 170.50/170.81 (step @p135 :rule refl :args (@t268)) % 170.50/170.81 (step @p136 :rule cong :premises (@p135 @p134) :args (@t281)) % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.50/170.81 (step @p137 :rule trust :premises () :args ((forall (@list @t282 @t283 @t284) (not (forall @t266 (not (forall @t265 (= @t264 (ite (= @t284 @t261) @t283 (_ @t225 @t282 @t261)))))))))) % 170.50/170.81 (step @p138 :rule instantiate :premises (@p137) :args ((@list @t224 @t226 @t209))) % 170.50/170.81 (step @p139 :rule refl :args (@t286)) % 170.50/170.81 (step @p140 :rule bool-double-not-elim :args (@t267)) % 170.50/170.81 (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or (not @t287) @t286))) % 170.50/170.81 (step @p142 :rule eq-symm :args (@t285 @t262)) % 170.50/170.81 (step @p143 :rule cong :premises (@p142) :args (@t288)) % 170.50/170.81 (step @p144 :rule bool-double-not-elim :args (@t288)) % 170.50/170.81 (step @p145 :rule trans :premises (@p144 @p143)) % 170.50/170.81 (step @p146 :rule refl :args (@t287)) % 170.50/170.81 (step @p147 :rule cong :premises (@p146 @p145) :args ((=> @t287 @t289))) % 170.50/170.81 (assume-push @p969 @t287) % 170.50/170.81 (step @p149 :rule skolemize :premises (@p138)) % 170.50/170.81 (step-pop @p970 :rule scope :premises (@p149)) % 170.50/170.81 (step @p150 :rule process_scope :premises (@p970) :args (@t289)) % 170.50/170.81 (step @p152 :rule eq_resolve :premises (@p150 @p147)) % 170.50/170.81 (step @p153 :rule implies_elim :premises (@p152)) % 170.50/170.81 (step @p154 :rule eq_resolve :premises (@p153 @p141)) % 170.50/170.81 (step @p155 :rule chain_m_resolution :premises (@p154 @p138) :args (@t286 @t247 (@list @t267))) % 170.50/170.81 (step @p156 :rule refl :args (@t281)) % 170.50/170.81 (step @p157 :rule ite-eq-branch :args (@t290 @t226)) % 170.50/170.81 (step @p158 :rule cong :premises (@p157 @p156) :args (@t291)) % 170.50/170.81 (step @p159 :rule cong :premises (@p139 @p158) :args ((=> @t286 @t291))) % 170.50/170.81 (assume-push @p971 @t286) % 170.50/170.81 (step @p161 :rule instantiate :premises (@p155) :args ((@list @t209))) % 170.50/170.81 (step-pop @p972 :rule scope :premises (@p161)) % 170.50/170.81 (step @p162 :rule process_scope :premises (@p972) :args (@t291)) % 170.50/170.81 (step @p164 :rule eq_resolve :premises (@p162 @p159)) % 170.50/170.81 (step @p165 :rule implies_elim :premises (@p164)) % 170.50/170.81 (step @p166 :rule chain_m_resolution :premises (@p165 @p155) :args ((= @t226 @t281) @t240 (@list @t286))) % 170.50/170.81 (step @p167 :rule symm :premises (@p133)) % 170.50/170.81 (step @p168 :rule trans :premises (@p130 @p167 @p8)) % 170.50/170.81 (step @p169 :rule cong :premises (@p81 @p168) :args (@t292)) % 170.50/170.81 (step @p170 :rule trans :premises (@p169 @p82 @p166 @p136)) % 170.50/170.81 (step @p171 :rule refl :args (@t294)) % 170.50/170.81 (step @p172 :rule bool-double-not-elim :args (@t269)) % 170.50/170.81 (step @p173 :rule nary_cong :premises (@p172 @p171) :args ((or (not @t295) @t294))) % 170.50/170.81 (assume-push @p973 @t295) % 170.50/170.81 (step @p175 :rule skolemize :premises (@p973)) % 170.50/170.81 (step-pop @p974 :rule scope :premises (@p175)) % 170.50/170.81 (step @p176 :rule process_scope :premises (@p974) :args (@t294)) % 170.50/170.81 (step @p178 :rule implies_elim :premises (@p176)) % 170.50/170.81 (step @p179 :rule eq_resolve :premises (@p178 @p173)) % 170.50/170.81 (step @p180 :rule chain_m_resolution :premises (@p179 @p170) :args (@t269 @t240 (@list @t293))) % 170.50/170.81 (step @p181 :rule cnf_or_pos :args (@t297)) % 170.50/170.81 (step @p182 :rule reordering :premises (@p181) :args ((or @t295 @t296 (not @t297)))) % 170.50/170.81 (step @p183 :rule chain_m_resolution :premises (@p182 @p180 @p102) :args (@t296 @t256 (@list @t269 @t297))) % 170.50/170.81 (step @p184 :rule eq-symm :args (@t330 @t227)) % 170.50/170.81 (step @p185 :rule cong :premises (@p184) :args (@t331)) % 170.50/170.81 (step @p186 :rule cong :premises (@p185) :args (@t332)) % 170.50/170.81 (step @p187 :rule cong :premises (@p186) :args (@t333)) % 170.50/170.81 (step @p188 :rule cong :premises (@p32 @p187) :args ((=> @t228 @t333))) % 170.50/170.81 (assume-push @p975 @t228) % 170.50/170.81 (step @p190 :rule instantiate :premises (@p27) :args (@t334)) % 170.50/170.81 (step-pop @p976 :rule scope :premises (@p190)) % 170.50/170.81 (step @p191 :rule process_scope :premises (@p976) :args (@t333)) % 170.50/170.81 (step @p193 :rule eq_resolve :premises (@p191 @p188)) % 170.50/170.81 (step @p194 :rule implies_elim :premises (@p193)) % 170.50/170.81 (step @p195 :rule chain_m_resolution :premises (@p194 @p27) :args (@t336 @t240 @t241)) % 170.50/170.81 (step @p196 :rule refl :args (@t339)) % 170.50/170.81 (step @p197 :rule bool-double-not-elim :args (@t335)) % 170.50/170.81 (step @p198 :rule nary_cong :premises (@p197 @p196) :args ((or (not @t336) @t339))) % 170.50/170.81 (step @p199 :rule eq-symm :args (@t338 @t330)) % 170.50/170.81 (step @p200 :rule bool-double-not-elim :args (@t340)) % 170.50/170.81 (step @p201 :rule trans :premises (@p200 @p199)) % 170.50/170.81 (step @p202 :rule refl :args (@t336)) % 170.50/170.81 (step @p203 :rule cong :premises (@p202 @p201) :args ((=> @t336 @t341))) % 170.50/170.81 (assume-push @p977 @t336) % 170.50/170.81 (step @p205 :rule skolemize :premises (@p195)) % 170.50/170.81 (step-pop @p978 :rule scope :premises (@p205)) % 170.50/170.81 (step @p206 :rule process_scope :premises (@p978) :args (@t341)) % 170.50/170.81 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 170.50/170.81 (step @p209 :rule implies_elim :premises (@p208)) % 170.50/170.81 (step @p210 :rule eq_resolve :premises (@p209 @p198)) % 170.50/170.81 (step @p211 :rule chain_m_resolution :premises (@p210 @p195) :args (@t339 @t247 (@list @t335))) % 170.50/170.81 (step @p212 :rule instantiate :premises (@p61) :args ((@list @t337))) % 170.50/170.81 (step @p213 :rule bool-double-not-elim :args (@t351)) % 170.50/170.81 (step @p214 :rule refl :args (@t366)) % 170.50/170.81 (step @p215 :rule nary_cong :premises (@p214 @p213) :args ((or @t366 (not @t363)))) % 170.50/170.81 (step @p216 :rule cnf_or_neg :args (@t366 2)) % 170.50/170.81 (step @p217 :rule eq_resolve :premises (@p216 @p215)) % 170.50/170.81 (step @p218 :rule reordering :premises (@p217) :args ((or @t351 @t366))) % 170.50/170.81 (step @p219 :rule bool-double-not-elim :args (@t361)) % 170.50/170.81 (step @p220 :rule nary_cong :premises (@p214 @p219) :args ((or @t366 (not @t362)))) % 170.50/170.81 (step @p221 :rule cnf_or_neg :args (@t366 3)) % 170.50/170.81 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 170.50/170.81 (step @p223 :rule reordering :premises (@p222) :args ((or @t361 @t366))) % 170.50/170.81 (step @p224 :rule bool-double-not-elim :args (@t359)) % 170.50/170.81 (step @p225 :rule nary_cong :premises (@p214 @p224) :args ((or @t366 (not @t360)))) % 170.50/170.81 (step @p226 :rule cnf_or_neg :args (@t366 4)) % 170.50/170.81 (step @p227 :rule eq_resolve :premises (@p226 @p225)) % 170.50/170.81 (step @p228 :rule reordering :premises (@p227) :args ((or @t359 @t366))) % 170.50/170.81 (step @p229 :rule bool-double-not-elim :args (@t357)) % 170.50/170.81 (step @p230 :rule nary_cong :premises (@p214 @p229) :args ((or @t366 (not @t358)))) % 170.50/170.81 (step @p231 :rule cnf_or_neg :args (@t366 5)) % 170.50/170.81 (step @p232 :rule eq_resolve :premises (@p231 @p230)) % 170.50/170.81 (step @p233 :rule reordering :premises (@p232) :args ((or @t357 @t366))) % 170.50/170.81 (step @p234 :rule cnf_or_neg :args (@t366 6)) % 170.50/170.81 (assume-push @p979 @t351) % 170.50/170.81 (step @p236 :rule instantiate :premises (@p979) :args ((@list @t209 @t352))) % 170.50/170.81 (step-pop @p980 :rule scope :premises (@p236)) % 170.50/170.81 (step @p237 :rule process_scope :premises (@p980) :args (@t375)) % 170.50/170.81 (step @p239 :rule implies_elim :premises (@p237)) % 170.50/170.81 (step @p240 :rule eq-symm :args (@t376 @t359)) % 170.50/170.81 (step @p241 :rule refl :args (@t361)) % 170.50/170.81 (step @p242 :rule cong :premises (@p241 @p240) :args ((=> @t361 @t377))) % 170.50/170.81 (assume-push @p981 @t361) % 170.50/170.81 (step @p244 :rule instantiate :premises (@p981) :args (@t378)) % 170.50/170.81 (step-pop @p982 :rule scope :premises (@p244)) % 170.50/170.81 (step @p245 :rule process_scope :premises (@p982) :args (@t377)) % 170.50/170.81 (step @p247 :rule eq_resolve :premises (@p245 @p242)) % 170.50/170.81 (step @p248 :rule implies_elim :premises (@p247)) % 170.50/170.81 (step @p249 :rule eq-symm :args (@t370 @t357)) % 170.50/170.81 (step @p250 :rule cong :premises (@p241 @p249) :args ((=> @t361 @t379))) % 170.50/170.81 (assume-push @p983 @t361) % 170.50/170.81 (step @p252 :rule instantiate :premises (@p983) :args ((@list @t352))) % 170.50/170.81 (step-pop @p984 :rule scope :premises (@p252)) % 170.50/170.81 (step @p253 :rule process_scope :premises (@p984) :args (@t379)) % 170.50/170.81 (step @p255 :rule eq_resolve :premises (@p253 @p250)) % 170.50/170.81 (step @p256 :rule implies_elim :premises (@p255)) % 170.50/170.81 (step @p257 :rule cnf_equiv_pos1 :args (@t380)) % 170.50/170.81 (step @p258 :rule reordering :premises (@p257) :args ((or @t360 @t376 (not @t380)))) % 170.50/170.81 (step @p259 :rule cnf_equiv_pos1 :args (@t381)) % 170.50/170.81 (step @p260 :rule reordering :premises (@p259) :args ((or @t358 @t370 (not @t381)))) % 170.50/170.81 (step @p261 :rule eq-symm :args (@t353 @t227)) % 170.50/170.81 (step @p262 :rule cong :premises (@p261) :args (@t382)) % 170.50/170.81 (step @p263 :rule cong :premises (@p262) :args (@t383)) % 170.50/170.81 (step @p264 :rule cong :premises (@p263) :args (@t384)) % 170.50/170.81 (step @p265 :rule cong :premises (@p32 @p264) :args ((=> @t228 @t384))) % 170.50/170.81 (assume-push @p985 @t228) % 170.50/170.81 (step @p267 :rule instantiate :premises (@p27) :args (@t378)) % 170.50/170.81 (step-pop @p986 :rule scope :premises (@p267)) % 170.50/170.81 (step @p268 :rule process_scope :premises (@p986) :args (@t384)) % 170.50/170.81 (step @p270 :rule eq_resolve :premises (@p268 @p265)) % 170.50/170.81 (step @p271 :rule implies_elim :premises (@p270)) % 170.50/170.81 (step @p272 :rule chain_m_resolution :premises (@p271 @p27) :args (@t386 @t240 @t241)) % 170.50/170.81 (step @p273 :rule refl :args (@t389)) % 170.50/170.81 (step @p274 :rule bool-double-not-elim :args (@t385)) % 170.50/170.81 (step @p275 :rule nary_cong :premises (@p274 @p273) :args ((or (not @t386) @t389))) % 170.50/170.81 (step @p276 :rule eq-symm :args (@t388 @t353)) % 170.50/170.81 (step @p277 :rule bool-double-not-elim :args (@t390)) % 170.50/170.81 (step @p278 :rule trans :premises (@p277 @p276)) % 170.50/170.81 (step @p279 :rule refl :args (@t386)) % 170.50/170.81 (step @p280 :rule cong :premises (@p279 @p278) :args ((=> @t386 @t391))) % 170.50/170.81 (assume-push @p987 @t386) % 170.50/170.81 (step @p282 :rule skolemize :premises (@p272)) % 170.50/170.81 (step-pop @p988 :rule scope :premises (@p282)) % 170.50/170.81 (step @p283 :rule process_scope :premises (@p988) :args (@t391)) % 170.50/170.81 (step @p285 :rule eq_resolve :premises (@p283 @p280)) % 170.50/170.81 (step @p286 :rule implies_elim :premises (@p285)) % 170.50/170.81 (step @p287 :rule eq_resolve :premises (@p286 @p275)) % 170.50/170.81 (step @p288 :rule chain_m_resolution :premises (@p287 @p272) :args (@t389 @t247 (@list @t385))) % 170.50/170.81 (step @p289 :rule instantiate :premises (@p61) :args ((@list @t387))) % 170.50/170.81 (assume-push @p989 @t376) % 170.50/170.81 (assume-push @p990 @t389) % 170.50/170.81 (assume-push @p991 @t392) % 170.50/170.81 (assume-push @p992 @t392) % 170.50/170.81 (assume-push @p993 @t389) % 170.50/170.81 (assume-push @p994 @t376) % 170.50/170.81 (step @p296 :rule true_intro :premises (@p989)) % 170.50/170.81 (step @p297 :rule refl :args (@t206)) % 170.50/170.81 (step @p298 :rule symm :premises (@p288)) % 170.50/170.81 (step @p299 :rule cong :premises (@p63 @p289) :args (@t209)) % 170.50/170.81 (step @p300 :rule trans :premises (@p299 @p298)) % 170.50/170.81 (step @p301 :rule refl :args (@t350)) % 170.50/170.81 (step @p302 :rule cong :premises (@p301 @p300) :args (@t372)) % 170.50/170.81 (step @p303 :rule cong :premises (@p302 @p297) :args (@t373)) % 170.50/170.81 (step @p304 :rule trans :premises (@p303 @p296)) % 170.50/170.81 (step @p305 :rule true_elim :premises (@p304)) % 170.50/170.81 (step-pop @p995 :rule scope :premises (@p305)) % 170.50/170.81 (step-pop @p996 :rule scope :premises (@p995)) % 170.50/170.81 (step-pop @p997 :rule scope :premises (@p996)) % 170.50/170.81 (step @p306 :rule process_scope :premises (@p997) :args (@t373)) % 170.50/170.81 (step @p310 :rule and_intro :premises (@p289 @p288 @p989)) % 170.50/170.81 (step @p311 :rule modus_ponens :premises (@p310 @p306)) % 170.50/170.81 (step-pop @p998 :rule scope :premises (@p311)) % 170.50/170.81 (step-pop @p999 :rule scope :premises (@p998)) % 170.50/170.81 (step-pop @p1000 :rule scope :premises (@p999)) % 170.50/170.81 (step @p312 :rule process_scope :premises (@p1000) :args (@t373)) % 170.50/170.81 (step @p316 :rule implies_elim :premises (@p312)) % 170.50/170.81 (step @p317 :rule cnf_and_neg :args (@t393)) % 170.50/170.81 (step @p318 :rule resolution :premises (@p317 @p316) :args (true @t393)) % 170.50/170.81 (step @p319 :rule reordering :premises (@p318) :args ((or @t373 (not @t376) @t395 @t394))) % 170.50/170.81 (step @p320 :rule cnf_or_pos :args (@t375)) % 170.50/170.81 (step @p321 :rule reordering :premises (@p320) :args ((or @t374 @t371 @t369 (not @t375)))) % 170.50/170.81 (step @p322 :rule eq-symm :args (@t396 @t356)) % 170.50/170.81 (step @p323 :rule cong :premises (@p241 @p322) :args ((=> @t361 @t397))) % 170.50/170.81 (assume-push @p1001 @t361) % 170.50/170.81 (step @p325 :rule instantiate :premises (@p1001) :args ((@list @t354))) % 170.50/170.81 (step-pop @p1002 :rule scope :premises (@p325)) % 170.50/170.81 (step @p326 :rule process_scope :premises (@p1002) :args (@t397)) % 170.50/170.81 (step @p328 :rule eq_resolve :premises (@p326 @p323)) % 170.50/170.81 (step @p329 :rule implies_elim :premises (@p328)) % 170.50/170.81 (step @p330 :rule cnf_equiv_pos2 :args (@t398)) % 170.50/170.81 (step @p331 :rule reordering :premises (@p330) :args ((or @t356 @t399 (not @t398)))) % 170.50/170.81 (step @p332 :rule bool-double-not-elim :args (@t396)) % 170.50/170.81 (step @p333 :rule refl :args (@t400)) % 170.50/170.81 (step @p334 :rule refl :args (@t394)) % 170.50/170.81 (step @p335 :rule refl :args (@t395)) % 170.50/170.81 (step @p336 :rule refl :args (@t401)) % 170.50/170.81 (step @p337 :rule nary_cong :premises (@p336 @p335 @p334 @p333 @p332) :args ((or @t401 @t395 @t394 @t400 (not @t399)))) % 170.50/170.81 (assume-push @p1003 @t399) % 170.50/170.81 (assume-push @p1004 @t389) % 170.50/170.81 (assume-push @p1005 @t392) % 170.50/170.81 (assume-push @p1006 @t214) % 170.50/170.81 (assume-push @p1007 @t369) % 170.50/170.81 (step @p343 :rule evaluate :args (@t402)) % 170.50/170.81 (step @p344 :rule false_intro :premises (@p1003)) % 170.50/170.81 (step @p297 :rule refl :args (@t206)) % 170.50/170.81 (step @p345 :rule refl :args (@t352)) % 170.50/170.81 (step @p298 :rule symm :premises (@p288)) % 170.50/170.81 (step @p299 :rule cong :premises (@p63 @p289) :args (@t209)) % 170.50/170.81 (step @p346 :rule trans :premises (@p80 @p299 @p298)) % 170.50/170.81 (step @p347 :rule cong :premises (@p81 @p346) :args (@t249)) % 170.50/170.81 (step @p348 :rule cong :premises (@p347 @p345) :args (@t367)) % 170.50/170.81 (step @p301 :rule refl :args (@t350)) % 170.50/170.81 (step @p349 :rule cong :premises (@p301 @p348) :args (@t368)) % 170.50/170.81 (step @p350 :rule cong :premises (@p349 @p297) :args (@t369)) % 170.50/170.81 (step @p351 :rule true_intro :premises (@p1007)) % 170.50/170.81 (step @p352 :rule symm :premises (@p351)) % 170.50/170.81 (step @p353 :rule trans :premises (@p352 @p350 @p344)) % 170.50/170.81 (step @p354 false :rule eq_resolve :premises (@p353 @p343)) % 170.50/170.81 (step-pop @p1008 :rule scope :premises (@p354)) % 170.50/170.81 (step-pop @p1009 :rule scope :premises (@p1008)) % 170.50/170.81 (step-pop @p1010 :rule scope :premises (@p1009)) % 170.50/170.81 (step-pop @p1011 :rule scope :premises (@p1010)) % 170.50/170.81 (step-pop @p1012 :rule scope :premises (@p1011)) % 170.50/170.81 (step @p355 :rule process_scope :premises (@p1012) :args (false)) % 170.50/170.81 (assume-push @p1013 @t214) % 170.50/170.81 (assume-push @p1014 @t389) % 170.50/170.81 (assume-push @p1015 @t392) % 170.50/170.81 (assume-push @p1016 @t369) % 170.50/170.81 (assume-push @p1017 @t399) % 170.50/170.81 (step @p366 :rule and_intro :premises (@p1017 @p288 @p289 @p8 @p1016)) % 170.50/170.81 (step-pop @p1018 :rule scope :premises (@p366)) % 170.50/170.81 (step-pop @p1019 :rule scope :premises (@p1018)) % 170.50/170.81 (step-pop @p1020 :rule scope :premises (@p1019)) % 170.50/170.81 (step-pop @p1021 :rule scope :premises (@p1020)) % 170.50/170.81 (step-pop @p1022 :rule scope :premises (@p1021)) % 170.50/170.81 (step @p367 :rule process_scope :premises (@p1022) :args (@t403)) % 170.50/170.81 (step @p373 :rule implies_elim :premises (@p367)) % 170.50/170.81 (step @p374 :rule resolution :premises (@p373 @p355) :args (true @t403)) % 170.50/170.81 (step @p375 :rule not_and :premises (@p374)) % 170.50/170.81 (step @p376 :rule eq_resolve :premises (@p375 @p337)) % 170.50/170.81 (step @p377 :rule chain_m_resolution :premises (@p376 @p289 @p288 @p8 @p331 @p329 @p321 @p319 @p289 @p288 @p260 @p258 @p256 @p248 @p239 @p234 @p233 @p228 @p223 @p218) :args (@t366 (@list false false false true false false false false false false false false false false true false false false false) (@list @t392 @t389 @t214 @t396 @t398 @t369 @t373 @t392 @t389 @t370 @t376 @t381 @t380 @t375 @t356 @t357 @t359 @t361 @t351))) % 170.50/170.81 (step @p378 :rule refl :args (@t404)) % 170.50/170.81 (step @p379 :rule bool-double-not-elim :args (@t348)) % 170.50/170.81 (step @p380 :rule nary_cong :premises (@p379 @p378) :args ((or (not @t405) @t404))) % 170.50/170.81 (assume-push @p1023 @t405) % 170.50/170.81 (step @p382 :rule skolemize :premises (@p1023)) % 170.50/170.81 (step-pop @p1024 :rule scope :premises (@p382)) % 170.50/170.81 (step @p383 :rule process_scope :premises (@p1024) :args (@t404)) % 170.50/170.81 (step @p385 :rule implies_elim :premises (@p383)) % 170.50/170.81 (step @p386 :rule eq_resolve :premises (@p385 @p380)) % 170.50/170.81 (step @p387 :rule chain_m_resolution :premises (@p386 @p377) :args (@t348 @t240 (@list @t366))) % 170.50/170.81 (step @p388 :rule refl :args (@t343)) % 170.50/170.81 (step @p389 :rule refl :args (@t344)) % 170.50/170.81 (step @p390 :rule refl :args (@t345)) % 170.50/170.81 (step @p391 :rule eq-symm :args (@t305 @t311)) % 170.50/170.81 (step @p392 :rule cong :premises (@p391) :args (@t406)) % 170.50/170.81 (step @p393 :rule cong :premises (@p392) :args (@t407)) % 170.50/170.81 (step @p394 :rule refl :args (@t346)) % 170.50/170.81 (step @p395 :rule refl :args (@t326)) % 170.50/170.81 (step @p396 :rule refl :args (@t327)) % 170.50/170.81 (step @p397 :rule nary_cong :premises (@p396 @p395 @p394 @p393 @p390 @p389 @p388) :args (@t408)) % 170.50/170.81 (step @p398 :rule cong :premises (@p397) :args (@t409)) % 170.50/170.81 (step @p399 :rule refl :args (@t302)) % 170.50/170.81 (step @p400 :rule refl :args (@t303)) % 170.50/170.81 (step @p401 :rule refl :args (@t304)) % 170.50/170.81 (step @p402 :rule refl :args (@t316)) % 170.50/170.81 (step @p403 :rule nary_cong :premises (@p396 @p395 @p402 @p393 @p401 @p400 @p399) :args (@t410)) % 170.50/170.81 (step @p404 :rule cong :premises (@p403) :args (@t411)) % 170.50/170.81 (step @p405 :rule cong :premises (@p404 @p398) :args ((= @t411 @t409))) % 170.50/170.81 (step @p406 :rule eq-symm :args (@t409 @t411)) % 170.50/170.81 (step @p407 :rule trans :premises (@p406 @p405)) % 170.50/170.81 (step @p408 :rule cong :premises (@p407) :args (@t412)) % 170.50/170.81 ; trust TRUST PREPROCESS_HO_ELIM % 170.50/170.81 (step @p409 :rule trust :premises () :args ((= (not (= @t438 (forall @t431 (or @t430 @t428 (not (forall @t32 (or @t421 @t420 (_ @t2 @t416 (tptp.hoasap @t416 @t8 @t416 @t24) @t416)))) @t419 @t415 @t414 @t413)))) @t412))) % 170.50/170.81 (step @p410 :rule refl :args (@t413)) % 170.50/170.81 (step @p411 :rule refl :args (@t414)) % 170.50/170.81 (step @p412 :rule refl :args (@t415)) % 170.50/170.81 (step @p413 :rule beta-reduce :args ((= @t439 @t418))) % 170.50/170.81 (step @p414 :rule cong :premises (@p413) :args (@t440)) % 170.50/170.81 (step @p415 :rule refl :args (@t416)) % 170.50/170.81 (step @p416 :rule refl :args (@t98)) % 170.50/170.81 (step @p417 :rule cong :premises (@p416 @p415) :args ((= @t98 @t416))) % 170.50/170.81 (step @p418 :rule symm :premises (@p417)) % 170.50/170.81 (step @p419 :rule eq_resolve :premises (@p416 @p418)) % 170.50/170.81 (step @p420 :rule refl :args (@t24)) % 170.50/170.81 (step @p421 :rule refl :args (@t8)) % 170.50/170.81 (step @p422 :rule cong :premises (@p419 @p421 @p419 @p420) :args (@t441)) % 170.50/170.81 (step @p423 :rule cong :premises (@p419 @p422 @p419) :args (@t442)) % 170.50/170.81 (step @p424 :rule cong :premises (@p419 @p420 @p419) :args (@t443)) % 170.50/170.81 (step @p425 :rule cong :premises (@p424) :args (@t444)) % 170.50/170.81 (step @p426 :rule cong :premises (@p419 @p421 @p419) :args (@t445)) % 170.50/170.81 (step @p427 :rule cong :premises (@p426) :args (@t446)) % 170.50/170.81 (step @p428 :rule nary_cong :premises (@p427 @p425 @p423) :args (@t447)) % 170.50/170.81 (step @p429 :rule cong :premises (@p428) :args (@t448)) % 170.50/170.81 (step @p430 :rule cong :premises (@p429) :args (@t449)) % 170.50/170.81 (step @p431 :rule refl :args (@t428)) % 170.50/170.81 (step @p432 :rule refl :args (@t430)) % 170.50/170.81 (step @p433 :rule nary_cong :premises (@p432 @p431 @p430 @p414 @p412 @p411 @p410) :args (@t450)) % 170.50/170.81 (step @p434 :rule cong :premises (@p433) :args (@t451)) % 170.50/170.81 (step @p435 :rule refl :args (@t438)) % 170.50/170.81 (step @p436 :rule cong :premises (@p435 @p434) :args (@t452)) % 170.50/170.81 (step @p437 :rule cong :premises (@p436) :args ((not @t452))) % 170.50/170.81 (step @p438 :rule refl :args (@t53)) % 170.50/170.81 (step @p439 :rule refl :args (@t2)) % 170.50/170.81 (step @p440 :rule refl :args (@t59)) % 170.50/170.81 (step @p441 :rule cong :premises (@p419 @p440 @p419) :args (@t453)) % 170.50/170.81 (step @p442 :rule refl :args (@t417)) % 170.50/170.81 (step @p443 :rule cong :premises (@p442 @p441) :args (@t454)) % 170.50/170.81 (step @p444 :rule cong :premises (@p443) :args (@t455)) % 170.50/170.81 (step @p445 :rule cong :premises (@p444) :args (@t456)) % 170.50/170.81 (step @p446 :rule refl :args (tptp.hoasinduction_p_and_p_prime)) % 170.50/170.81 (step @p447 :rule cong :premises (@p446 @p445) :args ((= tptp.hoasinduction_p_and_p_prime @t456))) % 170.50/170.81 (step @p448 :rule and_elim :premises (@p1) :args (10)) % 170.50/170.81 (step @p449 :rule refl :args (@t59)) % 170.50/170.81 (step @p450 :rule cong :premises (@p448 @p449 @p448) :args (@t457)) % 170.50/170.81 (step @p451 :rule refl :args (@t417)) % 170.50/170.81 (step @p452 :rule cong :premises (@p451 @p450) :args (@t458)) % 170.50/170.81 (step @p453 :rule cong :premises (@p452) :args (@t459)) % 170.50/170.81 (step @p454 :rule cong :premises (@p453) :args (@t460)) % 170.50/170.81 (step @p455 :rule cong :premises (@p446 @p454) :args ((= tptp.hoasinduction_p_and_p_prime @t460))) % 170.50/170.81 (step @p456 :rule trans :premises (@p455 @p447)) % 170.50/170.81 (step @p457 :rule refl :args (@t457)) % 170.50/170.81 (step @p458 :rule refl :args (@t60)) % 170.50/170.81 (step @p459 :rule cong :premises (@p458 @p457) :args ((= @t60 @t457))) % 170.50/170.81 (step @p460 :rule symm :premises (@p459)) % 170.50/170.81 (step @p461 :rule eq_resolve :premises (@p458 @p460)) % 170.50/170.81 (step @p462 :rule refl :args (@t417)) % 170.50/170.81 (step @p463 :rule refl :args (@t61)) % 170.50/170.81 (step @p464 :rule cong :premises (@p463 @p462) :args ((= @t61 @t417))) % 170.50/170.81 (step @p465 :rule symm :premises (@p464)) % 170.50/170.81 (step @p466 :rule eq_resolve :premises (@p463 @p465)) % 170.50/170.81 (step @p467 :rule cong :premises (@p466 @p461) :args (@t62)) % 170.50/170.81 (step @p468 :rule cong :premises (@p467) :args (@t64)) % 170.50/170.81 (step @p469 :rule cong :premises (@p468) :args (@t167)) % 170.50/170.81 (step @p470 :rule cong :premises (@p446 @p469) :args (@t168)) % 170.50/170.81 (step @p471 :rule and_elim :premises (@p1) :args (16)) % 170.50/170.81 (step @p472 :rule eq_resolve :premises (@p471 @p470)) % 170.50/170.81 (step @p473 :rule eq_resolve :premises (@p472 @p456)) % 170.50/170.81 (step @p474 :rule ho_cong :premises (@p473 @p439 @p438)) % 170.50/170.81 (step @p475 :rule cong :premises (@p474) :args (@t462)) % 170.50/170.81 (step @p476 :rule refl :args (@t24)) % 170.50/170.81 (step @p477 :rule refl :args (@t8)) % 170.50/170.81 (step @p478 :rule cong :premises (@p448 @p477 @p448 @p476) :args (@t463)) % 170.50/170.81 (step @p479 :rule cong :premises (@p448 @p478 @p448) :args (@t464)) % 170.50/170.81 (step @p480 :rule cong :premises (@p448 @p476 @p448) :args (@t465)) % 170.50/170.81 (step @p481 :rule cong :premises (@p480) :args (@t466)) % 170.50/170.81 (step @p482 :rule cong :premises (@p448 @p477 @p448) :args (@t467)) % 170.50/170.81 (step @p483 :rule cong :premises (@p482) :args (@t468)) % 170.50/170.81 (step @p484 :rule nary_cong :premises (@p483 @p481 @p479) :args (@t469)) % 170.50/170.81 (step @p485 :rule cong :premises (@p484) :args (@t470)) % 170.50/170.81 (step @p486 :rule cong :premises (@p485) :args (@t471)) % 170.50/170.81 (step @p487 :rule nary_cong :premises (@p432 @p431 @p486 @p475 @p412 @p411 @p410) :args (@t472)) % 170.50/170.81 (step @p488 :rule cong :premises (@p487) :args (@t473)) % 170.50/170.81 (step @p489 :rule refl :args (@t433)) % 170.50/170.81 (step @p490 :rule refl :args (@t435)) % 170.50/170.81 (step @p491 :rule refl :args (@t437)) % 170.50/170.81 (step @p492 :rule cong :premises (@p444) :args (@t474)) % 170.50/170.81 (step @p493 :rule cong :premises (@p421 @p419) :args (@t475)) % 170.50/170.81 (step @p494 :rule cong :premises (@p493 @p420) :args (@t476)) % 170.50/170.81 (step @p495 :rule cong :premises (@p419 @p494 @p419) :args (@t477)) % 170.50/170.81 (step @p496 :rule nary_cong :premises (@p427 @p425 @p495) :args (@t478)) % 170.50/170.81 (step @p497 :rule cong :premises (@p496) :args (@t479)) % 170.50/170.81 (step @p498 :rule cong :premises (@p497) :args (@t480)) % 170.50/170.81 (step @p499 :rule nary_cong :premises (@p432 @p431 @p498 @p492 @p491 @p490 @p489) :args (@t481)) % 170.50/170.81 (step @p500 :rule cong :premises (@p499) :args (@t482)) % 170.50/170.81 (step @p501 :rule refl :args (tptp.hoasinduction_lem2v2)) % 170.50/170.81 (step @p502 :rule cong :premises (@p501 @p500) :args ((= tptp.hoasinduction_lem2v2 @t482))) % 170.50/170.81 (step @p503 :rule cong :premises (@p453) :args (@t483)) % 170.50/170.81 (step @p504 :rule cong :premises (@p477 @p448) :args (@t484)) % 170.50/170.81 (step @p505 :rule cong :premises (@p504 @p476) :args (@t485)) % 170.50/170.81 (step @p506 :rule cong :premises (@p448 @p505 @p448) :args (@t486)) % 170.50/170.81 (step @p507 :rule nary_cong :premises (@p483 @p481 @p506) :args (@t487)) % 170.50/170.81 (step @p508 :rule cong :premises (@p507) :args (@t488)) % 170.50/170.81 (step @p509 :rule cong :premises (@p508) :args (@t489)) % 170.50/170.81 (step @p510 :rule nary_cong :premises (@p432 @p431 @p509 @p503 @p491 @p490 @p489) :args (@t490)) % 170.50/170.81 (step @p511 :rule cong :premises (@p510) :args (@t491)) % 170.50/170.81 (step @p512 :rule cong :premises (@p501 @p511) :args ((= tptp.hoasinduction_lem2v2 @t491))) % 170.50/170.81 (step @p513 :rule trans :premises (@p512 @p502)) % 170.50/170.81 (step @p514 :rule refl :args ((_ @t53 @t138))) % 170.50/170.81 (step @p515 :rule refl :args (@t432)) % 170.50/170.81 (step @p516 :rule cong :premises (@p515) :args (@t433)) % 170.50/170.81 (step @p517 :rule trans :premises (@p516 @p514)) % 170.50/170.81 (step @p518 :rule refl :args (@t53)) % 170.50/170.81 (step @p519 :rule ho_cong :premises (@p518 @p515)) % 170.50/170.81 (step @p520 :rule cong :premises (@p519 @p517) :args ((= (_ @t53 @t432) @t433))) % 170.50/170.81 (step @p521 :rule symm :premises (@p520)) % 170.50/170.81 (step @p522 :rule refl :args (@t139)) % 170.50/170.81 (step @p523 :rule eq_resolve :premises (@p522 @p521)) % 170.50/170.81 (step @p524 :rule refl :args (@t138)) % 170.50/170.81 (step @p525 :rule cong :premises (@p524 @p515) :args ((= @t138 @t432))) % 170.50/170.81 (step @p526 :rule symm :premises (@p525)) % 170.50/170.81 (step @p527 :rule eq_resolve :premises (@p524 @p526)) % 170.50/170.81 (step @p528 :rule ho_cong :premises (@p518 @p527)) % 170.50/170.81 (step @p529 :rule trans :premises (@p528 @p523)) % 170.50/170.81 (step @p530 :rule refl :args (@t434)) % 170.50/170.81 (step @p531 :rule refl :args (@t140)) % 170.50/170.81 (step @p532 :rule cong :premises (@p531 @p530) :args ((= @t140 @t434))) % 170.50/170.81 (step @p533 :rule symm :premises (@p532)) % 170.50/170.81 (step @p534 :rule eq_resolve :premises (@p531 @p533)) % 170.50/170.81 (step @p535 :rule cong :premises (@p534) :args (@t141)) % 170.50/170.81 (step @p536 :rule refl :args (@t436)) % 170.50/170.81 (step @p537 :rule refl :args (@t142)) % 170.50/170.81 (step @p538 :rule cong :premises (@p537 @p536) :args ((= @t142 @t436))) % 170.50/170.81 (step @p539 :rule symm :premises (@p538)) % 170.50/170.81 (step @p540 :rule eq_resolve :premises (@p537 @p539)) % 170.50/170.81 (step @p541 :rule cong :premises (@p540) :args (@t143)) % 170.50/170.81 (step @p542 :rule refl :args (@t483)) % 170.50/170.81 (step @p543 :rule refl :args (@t489)) % 170.50/170.81 (step @p544 :rule refl :args (@t428)) % 170.50/170.81 (step @p545 :rule refl :args (@t430)) % 170.50/170.81 (step @p546 :rule nary_cong :premises (@p545 @p544 @p543 @p542 @p541 @p535 @p529) :args (@t492)) % 170.50/170.81 (step @p547 :rule cong :premises (@p546) :args ((forall @t145 @t492))) % 170.50/170.81 (step @p548 :rule refl :args (@t139)) % 170.50/170.81 (step @p549 :rule refl :args (@t141)) % 170.50/170.81 (step @p550 :rule refl :args (@t143)) % 170.50/170.81 (step @p551 :rule cong :premises (@p468) :args (@t65)) % 170.50/170.81 (step @p552 :rule refl :args ((_ @t2 tptp.id @t27 tptp.id))) % 170.50/170.81 (step @p553 :rule refl :args (tptp.id)) % 170.50/170.81 (step @p554 :rule refl :args ((tptp.ap @t25 @t24))) % 170.50/170.81 (step @p555 :rule refl :args (@t484)) % 170.50/170.81 (step @p556 :rule cong :premises (@p555 @p420) :args (@t485)) % 170.50/170.81 (step @p557 :rule trans :premises (@p556 @p554)) % 170.50/170.81 (step @p558 :rule cong :premises (@p553 @p557 @p553) :args (@t486)) % 170.50/170.81 (step @p559 :rule trans :premises (@p558 @p552)) % 170.50/170.81 (step @p560 :rule refl :args (@t3)) % 170.50/170.81 (step @p561 :rule ho_cong :premises (@p560 @p557)) % 170.50/170.81 (step @p562 :rule ho_cong :premises (@p561 @p553)) % 170.50/170.81 (step @p563 :rule cong :premises (@p562 @p559) :args ((= (_ (_ @t3 @t485) tptp.id) @t486))) % 170.50/170.81 (step @p564 :rule symm :premises (@p563)) % 170.50/170.81 (step @p565 :rule refl :args (@t28)) % 170.50/170.81 (step @p566 :rule eq_resolve :premises (@p565 @p564)) % 170.50/170.81 (step @p567 :rule refl :args (tptp.ap)) % 170.50/170.81 (step @p568 :rule ho_cong :premises (@p567 @p555)) % 170.50/170.81 (step @p569 :rule ho_cong :premises (@p568 @p420)) % 170.50/170.81 (step @p570 :rule cong :premises (@p569 @p557) :args ((= (_ (_ tptp.ap @t484) @t24) @t485))) % 170.50/170.81 (step @p571 :rule symm :premises (@p570)) % 170.50/170.81 (step @p572 :rule refl :args (@t27)) % 170.50/170.81 (step @p573 :rule eq_resolve :premises (@p572 @p571)) % 170.50/170.81 (step @p574 :rule refl :args (@t25)) % 170.50/170.81 (step @p575 :rule cong :premises (@p574 @p555) :args ((= @t25 @t484))) % 170.50/170.81 (step @p576 :rule symm :premises (@p575)) % 170.50/170.81 (step @p577 :rule eq_resolve :premises (@p574 @p576)) % 170.50/170.81 (step @p578 :rule ho_cong :premises (@p567 @p577)) % 170.50/170.81 (step @p579 :rule ho_cong :premises (@p578 @p420)) % 170.50/170.81 (step @p580 :rule trans :premises (@p579 @p573)) % 170.50/170.81 (step @p581 :rule ho_cong :premises (@p560 @p580)) % 170.50/170.81 (step @p582 :rule ho_cong :premises (@p581 @p553)) % 170.50/170.81 (step @p583 :rule trans :premises (@p582 @p566)) % 170.50/170.81 (step @p584 :rule refl :args (@t465)) % 170.50/170.81 (step @p585 :rule refl :args (@t29)) % 170.50/170.81 (step @p586 :rule cong :premises (@p585 @p584) :args ((= @t29 @t465))) % 170.50/170.81 (step @p587 :rule symm :premises (@p586)) % 170.50/170.81 (step @p588 :rule eq_resolve :premises (@p585 @p587)) % 170.50/170.81 (step @p589 :rule cong :premises (@p588) :args (@t30)) % 170.50/170.81 (step @p590 :rule refl :args (@t467)) % 170.50/170.81 (step @p591 :rule refl :args (@t9)) % 170.50/170.81 (step @p592 :rule cong :premises (@p591 @p590) :args ((= @t9 @t467))) % 170.50/170.81 (step @p593 :rule symm :premises (@p592)) % 170.50/170.81 (step @p594 :rule eq_resolve :premises (@p591 @p593)) % 170.50/170.81 (step @p595 :rule cong :premises (@p594) :args (@t10)) % 170.50/170.81 (step @p596 :rule nary_cong :premises (@p595 @p589 @p583) :args (@t31)) % 170.50/170.81 (step @p597 :rule cong :premises (@p596) :args (@t33)) % 170.50/170.81 (step @p598 :rule cong :premises (@p597) :args (@t34)) % 170.50/170.81 (step @p599 :rule refl :args ((_ @t2 @t16 @t8 @t36))) % 170.50/170.81 (step @p600 :rule refl :args (@t422)) % 170.50/170.81 (step @p601 :rule refl :args (@t16)) % 170.50/170.81 (step @p602 :rule cong :premises (@p601 @p421 @p600) :args (@t423)) % 170.50/170.81 (step @p603 :rule trans :premises (@p602 @p599)) % 170.50/170.81 (step @p604 :rule refl :args (@t37)) % 170.50/170.81 (step @p605 :rule ho_cong :premises (@p604 @p600)) % 170.50/170.81 (step @p606 :rule cong :premises (@p605 @p603) :args ((= (_ @t37 @t422) @t423))) % 170.50/170.81 (step @p607 :rule symm :premises (@p606)) % 170.50/170.81 (step @p608 :rule refl :args (@t38)) % 170.50/170.81 (step @p609 :rule eq_resolve :premises (@p608 @p607)) % 170.50/170.81 (step @p610 :rule refl :args (@t36)) % 170.50/170.81 (step @p611 :rule cong :premises (@p610 @p600) :args ((= @t36 @t422))) % 170.50/170.81 (step @p612 :rule symm :premises (@p611)) % 170.50/170.81 (step @p613 :rule eq_resolve :premises (@p610 @p612)) % 170.50/170.81 (step @p614 :rule ho_cong :premises (@p604 @p613)) % 170.50/170.81 (step @p615 :rule trans :premises (@p614 @p609)) % 170.50/170.81 (step @p616 :rule refl :args ((_ @t2 @t40 @t39 @t13))) % 170.50/170.81 (step @p617 :rule refl :args (@t13)) % 170.50/170.81 (step @p618 :rule refl :args (@t424)) % 170.50/170.81 (step @p619 :rule refl :args (@t425)) % 170.50/170.81 (step @p620 :rule cong :premises (@p619 @p618 @p617) :args (@t426)) % 170.50/170.81 (step @p621 :rule trans :premises (@p620 @p616)) % 170.50/170.81 (step @p622 :rule refl :args (@t2)) % 170.50/170.81 (step @p623 :rule ho_cong :premises (@p622 @p619)) % 170.50/170.81 (step @p624 :rule ho_cong :premises (@p623 @p618)) % 170.50/170.81 (step @p625 :rule ho_cong :premises (@p624 @p617)) % 170.50/170.81 (step @p626 :rule cong :premises (@p625 @p621) :args ((= (_ (_ (_ @t2 @t425) @t424) @t13) @t426))) % 170.50/170.81 (step @p627 :rule symm :premises (@p626)) % 170.50/170.81 (step @p628 :rule refl :args (@t41)) % 170.50/170.81 (step @p629 :rule eq_resolve :premises (@p628 @p627)) % 170.50/170.81 (step @p630 :rule refl :args (@t39)) % 170.50/170.81 (step @p631 :rule cong :premises (@p630 @p618) :args ((= @t39 @t424))) % 170.50/170.81 (step @p632 :rule symm :premises (@p631)) % 170.50/170.81 (step @p633 :rule eq_resolve :premises (@p630 @p632)) % 170.50/170.81 (step @p634 :rule refl :args (@t40)) % 170.50/170.81 (step @p635 :rule cong :premises (@p634 @p619) :args ((= @t40 @t425))) % 170.50/170.81 (step @p636 :rule symm :premises (@p635)) % 170.50/170.81 (step @p637 :rule eq_resolve :premises (@p634 @p636)) % 170.50/170.81 (step @p638 :rule ho_cong :premises (@p622 @p637)) % 170.50/170.81 (step @p639 :rule ho_cong :premises (@p638 @p633)) % 170.50/170.81 (step @p640 :rule ho_cong :premises (@p639 @p617)) % 170.50/170.81 (step @p641 :rule trans :premises (@p640 @p629)) % 170.50/170.81 (step @p642 :rule cong :premises (@p641) :args (@t42)) % 170.50/170.81 (step @p643 :rule nary_cong :premises (@p642 @p615) :args (@t43)) % 170.50/170.81 (step @p644 :rule cong :premises (@p643) :args (@t45)) % 170.50/170.81 (step @p645 :rule cong :premises (@p644) :args (@t46)) % 170.50/170.81 (step @p646 :rule cong :premises (@p615) :args (@t47)) % 170.50/170.81 (step @p647 :rule nary_cong :premises (@p646 @p641) :args (@t48)) % 170.50/170.81 (step @p648 :rule cong :premises (@p647) :args (@t49)) % 170.50/170.81 (step @p649 :rule cong :premises (@p648) :args (@t50)) % 170.50/170.81 (step @p650 :rule nary_cong :premises (@p649 @p645 @p598 @p551 @p550 @p549 @p548) :args (@t144)) % 170.50/170.81 (step @p651 :rule cong :premises (@p650) :args (@t146)) % 170.50/170.81 (step @p652 :rule trans :premises (@p651 @p547)) % 170.50/170.81 (step @p653 :rule cong :premises (@p501 @p652) :args (@t147)) % 170.50/170.81 (step @p654 :rule and_elim :premises (@p1) :args (71)) % 170.50/170.81 (step @p655 :rule eq_resolve :premises (@p654 @p653)) % 170.50/170.81 (step @p656 :rule eq_resolve :premises (@p655 @p513)) % 170.50/170.81 (step @p657 :rule cong :premises (@p656 @p488) :args (@t493)) % 170.50/170.81 (step @p658 :rule cong :premises (@p657) :args ((not @t493))) % 170.50/170.81 (step @p659 :rule trans :premises (@p658 @p437)) % 170.50/170.81 (step @p660 :rule aci_norm :args ((= @t495 @t472))) % 170.50/170.81 (step @p661 :rule cong :premises (@p660) :args (@t496)) % 170.50/170.81 (step @p662 :rule quant-merge-prenex :args ((= (forall @t166 @t498) @t496))) % 170.50/170.81 (step @p663 :rule alpha_equiv :args (@t499 (@list @t299 @t298) (@list @t8 @t24))) % 170.50/170.81 (step @p664 :rule refl :args (@t462)) % 170.50/170.81 (step @p665 :rule refl :args (@t471)) % 170.50/170.81 (step @p666 :rule nary_cong :premises (@p545 @p544 @p665 @p664 @p663) :args (@t500)) % 170.50/170.81 (step @p667 :rule quant-miniscope-or :args ((= @t498 @t500))) % 170.50/170.81 (step @p668 :rule trans :premises (@p667 @p666)) % 170.50/170.81 (step @p669 :rule symm :premises (@p668)) % 170.50/170.81 (step @p670 :rule cong :premises (@p669) :args ((forall @t166 (or @t430 @t428 @t471 @t462 @t505)))) % 170.50/170.81 (step @p671 :rule trans :premises (@p670 @p662)) % 170.50/170.81 (step @p672 :rule trans :premises (@p671 @p661)) % 170.50/170.81 (step @p673 :rule refl :args (@t505)) % 170.50/170.81 (step @p674 :rule refl :args (@t461)) % 170.50/170.81 (step @p675 :rule refl :args (@t192)) % 170.50/170.81 (step @p676 :rule cong :premises (@p675 @p674) :args ((= @t192 @t461))) % 170.50/170.81 (step @p677 :rule symm :premises (@p676)) % 170.50/170.81 (step @p678 :rule eq_resolve :premises (@p675 @p677)) % 170.50/170.81 (step @p679 :rule cong :premises (@p678) :args (@t506)) % 170.50/170.81 (step @p680 :rule nary_cong :premises (@p545 @p544 @p665 @p679 @p673) :args (@t507)) % 170.50/170.81 (step @p681 :rule cong :premises (@p680) :args ((forall @t166 @t507))) % 170.50/170.81 (step @p682 :rule trans :premises (@p681 @p672)) % 170.50/170.81 (step @p683 :rule aci_norm :args ((= (or @t430 @t508) @t507))) % 170.50/170.81 (step @p684 :rule aci_norm :args ((= (or @t428 @t509) @t508))) % 170.50/170.81 (step @p685 :rule aci_norm :args ((= (or @t471 (or @t506 @t505)) @t509))) % 170.50/170.81 (step @p686 :rule bool-impl-elim :args (@t192 @t505)) % 170.50/170.81 (step @p687 :rule nary_cong :premises (@p665 @p686) :args ((or @t471 @t510))) % 170.50/170.81 (step @p688 :rule trans :premises (@p687 @p685)) % 170.50/170.81 (step @p689 :rule bool-impl-elim :args (@t470 @t510)) % 170.50/170.81 (step @p690 :rule trans :premises (@p689 @p688)) % 170.50/170.81 (step @p691 :rule nary_cong :premises (@p544 @p690) :args ((or @t428 @t511))) % 170.50/170.81 (step @p692 :rule trans :premises (@p691 @p684)) % 170.50/170.81 (step @p693 :rule bool-impl-elim :args (@t427 @t511)) % 170.50/170.81 (step @p694 :rule trans :premises (@p693 @p692)) % 170.50/170.81 (step @p695 :rule nary_cong :premises (@p545 @p694) :args ((or @t430 @t512))) % 170.50/170.81 (step @p696 :rule trans :premises (@p695 @p683)) % 170.50/170.81 (step @p697 :rule bool-impl-elim :args (@t429 @t512)) % 170.50/170.81 (step @p698 :rule trans :premises (@p697 @p696)) % 170.50/170.81 (step @p699 :rule cong :premises (@p698) :args ((forall @t166 (=> @t429 @t512)))) % 170.50/170.81 (step @p700 :rule trans :premises (@p699 @p682)) % 170.50/170.81 (step @p701 :rule refl :args ((_ @t53 @t75))) % 170.50/170.81 (step @p702 :rule refl :args (@t501)) % 170.50/170.81 (step @p703 :rule cong :premises (@p702) :args (@t502)) % 170.50/170.81 (step @p704 :rule trans :premises (@p703 @p701)) % 170.50/170.81 (step @p705 :rule ho_cong :premises (@p518 @p702)) % 170.50/170.81 (step @p706 :rule cong :premises (@p705 @p704) :args ((= (_ @t53 @t501) @t502))) % 170.50/170.81 (step @p707 :rule symm :premises (@p706)) % 170.50/170.81 (step @p708 :rule refl :args (@t188)) % 170.50/170.81 (step @p709 :rule eq_resolve :premises (@p708 @p707)) % 170.50/170.81 (step @p710 :rule refl :args (@t75)) % 170.50/170.81 (step @p711 :rule cong :premises (@p710 @p702) :args ((= @t75 @t501))) % 170.50/170.81 (step @p712 :rule symm :premises (@p711)) % 170.50/170.81 (step @p713 :rule eq_resolve :premises (@p710 @p712)) % 170.50/170.81 (step @p714 :rule ho_cong :premises (@p518 @p713)) % 170.50/170.81 (step @p715 :rule trans :premises (@p714 @p709)) % 170.50/170.81 (step @p716 :rule refl :args (@t503)) % 170.50/170.81 (step @p717 :rule refl :args (@t56)) % 170.50/170.81 (step @p718 :rule cong :premises (@p717 @p716) :args ((= @t56 @t503))) % 170.50/170.81 (step @p719 :rule symm :premises (@p718)) % 170.50/170.81 (step @p720 :rule eq_resolve :premises (@p717 @p719)) % 170.50/170.81 (step @p721 :rule cong :premises (@p720) :args (@t57)) % 170.50/170.81 (step @p722 :rule refl :args (@t504)) % 170.50/170.81 (step @p723 :rule refl :args (@t190)) % 170.50/170.81 (step @p724 :rule cong :premises (@p723 @p722) :args ((= @t190 @t504))) % 170.50/170.81 (step @p725 :rule symm :premises (@p724)) % 170.50/170.81 (step @p726 :rule eq_resolve :premises (@p723 @p725)) % 170.50/170.81 (step @p727 :rule cong :premises (@p726) :args (@t513)) % 170.50/170.81 (step @p728 :rule nary_cong :premises (@p727 @p721 @p715) :args (@t514)) % 170.50/170.81 (step @p729 :rule cong :premises (@p728) :args ((forall @t32 @t514))) % 170.50/170.81 (step @p730 :rule aci_norm :args ((= (or @t513 (or @t57 @t188)) @t514))) % 170.50/170.81 (step @p731 :rule bool-impl-elim :args (@t56 @t188)) % 170.50/170.81 (step @p732 :rule refl :args (@t513)) % 170.50/170.81 (step @p733 :rule nary_cong :premises (@p732 @p731) :args ((or @t513 @t189))) % 170.50/170.81 (step @p734 :rule trans :premises (@p733 @p730)) % 170.50/170.81 (step @p735 :rule bool-impl-elim :args (@t190 @t189)) % 170.50/170.81 (step @p736 :rule trans :premises (@p735 @p734)) % 170.50/170.81 (step @p737 :rule cong :premises (@p736) :args (@t191)) % 170.50/170.81 (step @p738 :rule trans :premises (@p737 @p729)) % 170.50/170.81 (step @p739 :rule refl :args (@t192)) % 170.50/170.81 (step @p740 :rule cong :premises (@p739 @p738) :args (@t193)) % 170.50/170.81 (step @p741 :rule refl :args ((_ @t2 tptp.id @t194 tptp.id))) % 170.50/170.81 (step @p742 :rule refl :args (@t463)) % 170.50/170.81 (step @p743 :rule cong :premises (@p553 @p742 @p553) :args (@t464)) % 170.50/170.81 (step @p744 :rule trans :premises (@p743 @p741)) % 170.50/170.81 (step @p745 :rule ho_cong :premises (@p560 @p742)) % 170.50/170.81 (step @p746 :rule ho_cong :premises (@p745 @p553)) % 170.50/170.81 (step @p747 :rule cong :premises (@p746 @p744) :args ((= (_ (_ @t3 @t463) tptp.id) @t464))) % 170.50/170.81 (step @p748 :rule symm :premises (@p747)) % 170.50/170.81 (step @p749 :rule refl :args (@t195)) % 170.50/170.81 (step @p750 :rule eq_resolve :premises (@p749 @p748)) % 170.50/170.81 (step @p751 :rule refl :args (@t194)) % 170.50/170.81 (step @p752 :rule cong :premises (@p751 @p742) :args ((= @t194 @t463))) % 170.50/170.81 (step @p753 :rule symm :premises (@p752)) % 170.50/170.81 (step @p754 :rule eq_resolve :premises (@p751 @p753)) % 170.50/170.81 (step @p755 :rule ho_cong :premises (@p560 @p754)) % 170.50/170.81 (step @p756 :rule ho_cong :premises (@p755 @p553)) % 170.50/170.81 (step @p757 :rule trans :premises (@p756 @p750)) % 170.50/170.81 (step @p758 :rule nary_cong :premises (@p595 @p589 @p757) :args (@t515)) % 170.50/170.81 (step @p759 :rule cong :premises (@p758) :args ((forall @t32 @t515))) % 170.50/170.81 (step @p760 :rule aci_norm :args ((= (or @t10 (or @t30 @t195)) @t515))) % 170.50/170.81 (step @p761 :rule bool-impl-elim :args (@t29 @t195)) % 170.50/170.81 (step @p762 :rule refl :args (@t10)) % 170.50/170.81 (step @p763 :rule nary_cong :premises (@p762 @p761) :args ((or @t10 @t196))) % 170.50/170.81 (step @p764 :rule trans :premises (@p763 @p760)) % 170.50/170.81 (step @p765 :rule bool-impl-elim :args (@t9 @t196)) % 170.50/170.81 (step @p766 :rule trans :premises (@p765 @p764)) % 170.50/170.81 (step @p767 :rule cong :premises (@p766) :args (@t197)) % 170.50/170.81 (step @p768 :rule trans :premises (@p767 @p759)) % 170.50/170.81 (step @p769 :rule cong :premises (@p768 @p740) :args (@t198)) % 170.50/170.81 (step @p770 :rule bool-impl-elim :args (@t41 @t38)) % 170.50/170.81 (step @p771 :rule cong :premises (@p770) :args (@t199)) % 170.50/170.81 (step @p772 :rule trans :premises (@p771 @p644)) % 170.50/170.81 (step @p773 :rule cong :premises (@p772 @p769) :args (@t200)) % 170.50/170.81 (step @p774 :rule bool-impl-elim :args (@t38 @t41)) % 170.50/170.81 (step @p775 :rule cong :premises (@p774) :args (@t201)) % 170.50/170.81 (step @p776 :rule trans :premises (@p775 @p648)) % 170.50/170.81 (step @p777 :rule cong :premises (@p776 @p773) :args (@t202)) % 170.50/170.81 (step @p778 :rule cong :premises (@p777) :args (@t203)) % 170.50/170.81 (step @p779 :rule trans :premises (@p778 @p700)) % 170.50/170.81 (step @p780 :rule cong :premises (@p501 @p779) :args (@t204)) % 170.50/170.81 (step @p781 :rule cong :premises (@p780) :args (@t205)) % 170.50/170.81 (step @p782 :rule trans :premises (@p781 @p659 @p409 @p408)) % 170.50/170.81 (step @p783 :rule eq_resolve :premises (@p2 @p782)) % 170.50/170.81 (step @p784 :rule not_equiv_elim2 :premises (@p783)) % 170.50/170.81 (step @p785 :rule chain_m_resolution :premises (@p784 @p387) :args (@t516 @t240 (@list @t348))) % 170.50/170.81 (step @p786 :rule refl :args (@t534)) % 170.50/170.81 (step @p787 :rule bool-double-not-elim :args (@t329)) % 170.50/170.81 (step @p788 :rule nary_cong :premises (@p787 @p786) :args ((or (not @t516) @t534))) % 170.50/170.81 (assume-push @p1025 @t516) % 170.50/170.81 (step @p790 :rule skolemize :premises (@p1025)) % 170.50/170.81 (step-pop @p1026 :rule scope :premises (@p790)) % 170.50/170.81 (step @p791 :rule process_scope :premises (@p1026) :args (@t534)) % 170.50/170.81 (step @p793 :rule implies_elim :premises (@p791)) % 170.50/170.81 (step @p794 :rule eq_resolve :premises (@p793 @p788)) % 170.50/170.81 (step @p795 :rule chain_m_resolution :premises (@p794 @p785) :args (@t534 @t247 (@list @t329))) % 170.50/170.81 (step @p796 :rule bool-double-not-elim :args (@t529)) % 170.50/170.81 (step @p797 :rule refl :args (@t533)) % 170.50/170.81 (step @p798 :rule nary_cong :premises (@p797 @p796) :args ((or @t533 (not @t530)))) % 170.50/170.81 (step @p799 :rule cnf_or_neg :args (@t533 2)) % 170.50/170.81 (step @p800 :rule eq_resolve :premises (@p799 @p798)) % 170.50/170.81 (step @p801 :rule reordering :premises (@p800) :args ((or @t529 @t533))) % 170.50/170.81 (step @p802 :rule chain_m_resolution :premises (@p801 @p795) :args (@t529 @t247 @t535)) % 170.50/170.81 (assume-push @p1027 @t529) % 170.50/170.81 (step @p804 :rule instantiate :premises (@p1027) :args ((@list @t209 @t517))) % 170.50/170.81 (step-pop @p1028 :rule scope :premises (@p804)) % 170.50/170.81 (step @p805 :rule process_scope :premises (@p1028) :args (@t544)) % 170.50/170.81 (step @p807 :rule implies_elim :premises (@p805)) % 170.50/170.81 (step @p808 :rule chain_m_resolution :premises (@p807 @p802) :args (@t544 @t240 (@list @t529))) % 170.50/170.81 (step @p809 :rule bool-double-not-elim :args (@t527)) % 170.50/170.81 (step @p810 :rule nary_cong :premises (@p797 @p809) :args ((or @t533 (not @t528)))) % 170.50/170.81 (step @p811 :rule cnf_or_neg :args (@t533 3)) % 170.50/170.81 (step @p812 :rule eq_resolve :premises (@p811 @p810)) % 170.50/170.81 (step @p813 :rule reordering :premises (@p812) :args ((or @t527 @t533))) % 170.50/170.81 (step @p814 :rule chain_m_resolution :premises (@p813 @p795) :args (@t527 @t247 @t535)) % 170.50/170.81 (step @p815 :rule eq-symm :args (@t539 @t521)) % 170.50/170.81 (step @p816 :rule refl :args (@t527)) % 170.50/170.81 (step @p817 :rule cong :premises (@p816 @p815) :args ((=> @t527 @t545))) % 170.50/170.81 (assume-push @p1029 @t527) % 170.50/170.81 (step @p819 :rule instantiate :premises (@p1029) :args ((@list @t517))) % 170.50/170.81 (step-pop @p1030 :rule scope :premises (@p819)) % 170.50/170.81 (step @p820 :rule process_scope :premises (@p1030) :args (@t545)) % 170.50/170.81 (step @p822 :rule eq_resolve :premises (@p820 @p817)) % 170.50/170.81 (step @p823 :rule implies_elim :premises (@p822)) % 170.50/170.81 (step @p824 :rule chain_m_resolution :premises (@p823 @p814) :args (@t546 @t240 @t547)) % 170.50/170.81 (step @p825 :rule bool-double-not-elim :args (@t521)) % 170.50/170.81 (step @p826 :rule nary_cong :premises (@p797 @p825) :args ((or @t533 (not @t522)))) % 170.50/170.81 (step @p827 :rule cnf_or_neg :args (@t533 5)) % 170.50/170.81 (step @p828 :rule eq_resolve :premises (@p827 @p826)) % 170.50/170.81 (step @p829 :rule reordering :premises (@p828) :args ((or @t521 @t533))) % 170.50/170.81 (step @p830 :rule chain_m_resolution :premises (@p829 @p795) :args (@t521 @t247 @t535)) % 170.50/170.81 (step @p831 :rule cnf_equiv_pos1 :args (@t546)) % 170.50/170.81 (step @p832 :rule reordering :premises (@p831) :args ((or @t522 @t539 (not @t546)))) % 170.50/170.81 (step @p833 :rule chain_m_resolution :premises (@p832 @p830 @p824) :args (@t539 @t256 (@list @t521 @t546))) % 170.50/170.81 (step @p834 :rule eq-symm :args (@t548 @t523)) % 170.50/170.81 (step @p835 :rule cong :premises (@p816 @p834) :args ((=> @t527 @t549))) % 170.50/170.81 (assume-push @p1031 @t527) % 170.50/170.81 (step @p837 :rule instantiate :premises (@p1031) :args (@t334)) % 170.50/170.81 (step-pop @p1032 :rule scope :premises (@p837)) % 170.50/170.81 (step @p838 :rule process_scope :premises (@p1032) :args (@t549)) % 170.50/170.81 (step @p840 :rule eq_resolve :premises (@p838 @p835)) % 170.50/170.81 (step @p841 :rule implies_elim :premises (@p840)) % 170.50/170.81 (step @p842 :rule chain_m_resolution :premises (@p841 @p814) :args (@t550 @t240 @t547)) % 170.50/170.81 (step @p843 :rule bool-double-not-elim :args (@t523)) % 170.50/170.81 (step @p844 :rule nary_cong :premises (@p797 @p843) :args ((or @t533 (not @t524)))) % 170.50/170.81 (step @p845 :rule cnf_or_neg :args (@t533 4)) % 170.50/170.81 (step @p846 :rule eq_resolve :premises (@p845 @p844)) % 170.50/170.81 (step @p847 :rule reordering :premises (@p846) :args ((or @t523 @t533))) % 170.50/170.81 (step @p848 :rule chain_m_resolution :premises (@p847 @p795) :args (@t523 @t247 @t535)) % 170.50/170.81 (step @p849 :rule cnf_equiv_pos1 :args (@t550)) % 170.50/170.81 (step @p850 :rule reordering :premises (@p849) :args ((or @t524 @t548 (not @t550)))) % 170.50/170.81 (step @p851 :rule chain_m_resolution :premises (@p850 @p848 @p842) :args (@t548 @t256 (@list @t523 @t550))) % 170.50/170.81 (assume-push @p1033 @t548) % 170.50/170.81 (assume-push @p1034 @t339) % 170.50/170.81 (assume-push @p1035 @t551) % 170.50/170.81 (assume-push @p1036 @t551) % 170.50/170.81 (assume-push @p1037 @t339) % 170.50/170.81 (assume-push @p1038 @t548) % 170.50/170.81 (step @p858 :rule true_intro :premises (@p1033)) % 170.50/170.81 (step @p297 :rule refl :args (@t206)) % 170.50/170.81 (step @p859 :rule symm :premises (@p211)) % 170.50/170.81 (step @p860 :rule cong :premises (@p63 @p212) :args (@t209)) % 170.50/170.81 (step @p861 :rule trans :premises (@p860 @p859)) % 170.50/170.81 (step @p862 :rule refl :args (@t526)) % 170.50/170.81 (step @p863 :rule cong :premises (@p862 @p861) :args (@t541)) % 170.50/170.81 (step @p864 :rule cong :premises (@p863 @p297) :args (@t542)) % 170.50/170.81 (step @p865 :rule trans :premises (@p864 @p858)) % 170.50/170.81 (step @p866 :rule true_elim :premises (@p865)) % 170.50/170.81 (step-pop @p1039 :rule scope :premises (@p866)) % 170.50/170.81 (step-pop @p1040 :rule scope :premises (@p1039)) % 170.50/170.81 (step-pop @p1041 :rule scope :premises (@p1040)) % 170.50/170.81 (step @p867 :rule process_scope :premises (@p1041) :args (@t542)) % 170.50/170.81 (step @p871 :rule and_intro :premises (@p212 @p211 @p1033)) % 170.50/170.81 (step @p872 :rule modus_ponens :premises (@p871 @p867)) % 170.50/170.81 (step-pop @p1042 :rule scope :premises (@p872)) % 170.50/170.81 (step-pop @p1043 :rule scope :premises (@p1042)) % 170.50/170.81 (step-pop @p1044 :rule scope :premises (@p1043)) % 170.50/170.81 (step @p873 :rule process_scope :premises (@p1044) :args (@t542)) % 170.50/170.81 (step @p877 :rule implies_elim :premises (@p873)) % 170.50/170.81 (step @p878 :rule cnf_and_neg :args (@t552)) % 170.50/170.81 (step @p879 :rule resolution :premises (@p878 @p877) :args (true @t552)) % 170.50/170.81 (step @p880 :rule reordering :premises (@p879) :args ((or @t542 (not @t548) @t554 @t553))) % 170.50/170.81 (step @p881 :rule chain_m_resolution :premises (@p880 @p851 @p211 @p212) :args (@t542 @t555 (@list @t548 @t339 @t551))) % 170.50/170.81 (step @p882 :rule cnf_or_pos :args (@t544)) % 170.50/170.81 (step @p883 :rule reordering :premises (@p882) :args ((or @t543 @t540 @t538 (not @t544)))) % 170.50/170.81 (step @p884 :rule chain_m_resolution :premises (@p883 @p881 @p833 @p808) :args (@t538 @t555 (@list @t542 @t539 @t544))) % 170.50/170.81 (step @p885 :rule eq-symm :args (@t556 @t520)) % 170.50/170.81 (step @p886 :rule cong :premises (@p816 @p885) :args ((=> @t527 @t557))) % 170.50/170.81 (assume-push @p1045 @t527) % 170.50/170.81 (step @p888 :rule instantiate :premises (@p1045) :args ((@list @t518))) % 170.50/170.81 (step-pop @p1046 :rule scope :premises (@p888)) % 170.50/170.81 (step @p889 :rule process_scope :premises (@p1046) :args (@t557)) % 170.50/170.81 (step @p891 :rule eq_resolve :premises (@p889 @p886)) % 170.50/170.81 (step @p892 :rule implies_elim :premises (@p891)) % 170.50/170.81 (step @p893 :rule chain_m_resolution :premises (@p892 @p814) :args (@t558 @t240 @t547)) % 170.50/170.81 (step @p894 :rule cnf_or_neg :args (@t533 6)) % 170.50/170.81 (step @p895 :rule chain_m_resolution :premises (@p894 @p795) :args ((not @t520) @t247 @t535)) % 170.50/170.81 (step @p896 :rule cnf_equiv_pos2 :args (@t558)) % 170.50/170.81 (step @p897 :rule reordering :premises (@p896) :args ((or @t520 @t559 (not @t558)))) % 170.50/170.81 (step @p898 :rule chain_m_resolution :premises (@p897 @p895 @p893) :args (@t559 (@list true false) (@list @t520 @t558))) % 170.50/170.81 (step @p899 :rule bool-double-not-elim :args (@t556)) % 170.50/170.81 (step @p900 :rule refl :args (@t560)) % 170.50/170.81 (step @p901 :rule refl :args (@t553)) % 170.50/170.81 (step @p902 :rule refl :args (@t554)) % 170.50/170.81 (step @p903 :rule refl :args (@t561)) % 170.50/170.81 (step @p904 :rule refl :args (@t562)) % 170.50/170.81 (step @p905 :rule nary_cong :premises (@p336 @p904 @p903 @p902 @p901 @p900 @p899) :args ((or @t401 @t562 @t561 @t554 @t553 @t560 (not @t559)))) % 170.50/170.81 (assume-push @p1047 @t559) % 170.50/170.81 (assume-push @p1048 @t296) % 170.50/170.81 (assume-push @p1049 @t339) % 170.50/170.81 (assume-push @p1050 @t551) % 170.50/170.81 (assume-push @p1051 @t214) % 170.50/170.81 (assume-push @p1052 @t254) % 170.50/170.81 (assume-push @p1053 @t538) % 170.50/170.81 (step @p343 :rule evaluate :args (@t402)) % 170.50/170.81 (step @p913 :rule false_intro :premises (@p1047)) % 170.50/170.82 (step @p297 :rule refl :args (@t206)) % 170.50/170.82 (step @p914 :rule refl :args (@t517)) % 170.50/170.82 (step @p915 :rule refl :args (@t330)) % 170.50/170.82 (step @p916 :rule symm :premises (@p1048)) % 170.50/170.82 (step @p917 :rule cong :premises (@p916 @p915) :args ((_ @t225 @t268 @t330))) % 170.50/170.82 (step @p859 :rule symm :premises (@p211)) % 170.50/170.82 (step @p860 :rule cong :premises (@p63 @p212) :args (@t209)) % 170.50/170.82 (step @p918 :rule trans :premises (@p80 @p860 @p859)) % 170.50/170.82 (step @p919 :rule cong :premises (@p1048 @p918) :args (@t249)) % 170.50/170.82 (step @p920 :rule trans :premises (@p85 @p919 @p917)) % 170.50/170.82 (step @p921 :rule symm :premises (@p1052)) % 170.50/170.82 (step @p922 :rule trans :premises (@p921 @p920)) % 170.50/170.82 (step @p923 :rule cong :premises (@p922 @p914) :args (@t536)) % 170.50/170.82 (step @p862 :rule refl :args (@t526)) % 170.50/170.82 (step @p924 :rule cong :premises (@p862 @p923) :args (@t537)) % 170.50/170.82 (step @p925 :rule cong :premises (@p924 @p297) :args (@t538)) % 170.50/170.82 (step @p926 :rule true_intro :premises (@p1053)) % 170.50/170.82 (step @p927 :rule symm :premises (@p926)) % 170.50/170.82 (step @p928 :rule trans :premises (@p927 @p925 @p913)) % 170.50/170.82 (step @p929 false :rule eq_resolve :premises (@p928 @p343)) % 170.50/170.82 (step-pop @p1054 :rule scope :premises (@p929)) % 170.50/170.82 (step-pop @p1055 :rule scope :premises (@p1054)) % 170.50/170.82 (step-pop @p1056 :rule scope :premises (@p1055)) % 170.50/170.82 (step-pop @p1057 :rule scope :premises (@p1056)) % 170.50/170.82 (step-pop @p1058 :rule scope :premises (@p1057)) % 170.50/170.82 (step-pop @p1059 :rule scope :premises (@p1058)) % 170.50/170.82 (step-pop @p1060 :rule scope :premises (@p1059)) % 170.50/170.82 (step @p930 :rule process_scope :premises (@p1060) :args (false)) % 170.50/170.82 (assume-push @p1061 @t214) % 170.50/170.82 (assume-push @p1062 @t254) % 170.50/170.82 (assume-push @p1063 @t296) % 170.50/170.82 (assume-push @p1064 @t339) % 170.50/170.82 (assume-push @p1065 @t551) % 170.50/170.82 (assume-push @p1066 @t538) % 170.50/170.82 (assume-push @p1067 @t559) % 170.50/170.82 (step @p945 :rule and_intro :premises (@p1067 @p1063 @p211 @p212 @p8 @p1062 @p1066)) % 170.50/170.82 (step-pop @p1068 :rule scope :premises (@p945)) % 170.50/170.82 (step-pop @p1069 :rule scope :premises (@p1068)) % 170.50/170.82 (step-pop @p1070 :rule scope :premises (@p1069)) % 170.50/170.82 (step-pop @p1071 :rule scope :premises (@p1070)) % 170.50/170.82 (step-pop @p1072 :rule scope :premises (@p1071)) % 170.50/170.82 (step-pop @p1073 :rule scope :premises (@p1072)) % 170.50/170.82 (step-pop @p1074 :rule scope :premises (@p1073)) % 170.50/170.82 (step @p946 :rule process_scope :premises (@p1074) :args (@t563)) % 170.50/170.82 (step @p954 :rule implies_elim :premises (@p946)) % 170.50/170.82 (step @p955 :rule resolution :premises (@p954 @p930) :args (true @t563)) % 170.50/170.82 (step @p956 :rule not_and :premises (@p955)) % 170.50/170.82 (step @p957 :rule eq_resolve :premises (@p956 @p905)) % 170.50/170.82 (step @p958 false :rule chain_m_resolution :premises (@p957 @p898 @p884 @p212 @p211 @p183 @p100 @p8) :args (false (@list true false false false false false false) (@list @t556 @t538 @t551 @t339 @t296 @t254 @t214))) % 170.50/170.82 ) % 170.50/170.82 % SZS output end Proof % 170.50/170.82 % cvc5 exiting %------------------------------------------------------------------------------