%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n012.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 168.77s 169.04s % Output : Proof 168.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 23:02:33 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.37 %----Proving TH0 % 168.77/169.04 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 168.77/169.04 --- 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... % 168.77/169.04 --- 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... % 168.77/169.04 --- Run --ho-elim --full-saturate-quant at 18s... % 168.77/169.04 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 168.77/169.04 % SZS status Theorem % 168.77/169.04 % SZS output start Proof % 168.77/169.04 ( % 168.77/169.04 (declare-sort tptp.term 0) % 168.77/169.04 (declare-sort tptp.subst 0) % 168.77/169.04 (declare-sort tptp.d_term 0) % 168.77/169.04 (declare-sort tptp.d_subst 0) % 168.77/169.04 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 168.77/169.04 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 168.77/169.04 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 168.77/169.04 (declare-const tptp.pushprop_lem1v2 Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem1_gthm Bool) % 168.77/169.04 (declare-const tptp.axmap Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem0_gthm Bool) % 168.77/169.04 (declare-const tptp.shinj Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem1v2 Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 168.77/169.04 (declare-const tptp.induction2lem Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 168.77/169.04 (declare-const tptp.axvarshift Bool) % 168.77/169.04 (declare-const tptp.hoasapinj2 Bool) % 168.77/169.04 (declare-const tptp.hoasapnotvar_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasapinj1 Bool) % 168.77/169.04 (declare-const tptp.ulamvar1 Bool) % 168.77/169.04 (declare-const tptp.induction2lem_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 168.77/169.04 (declare-const tptp.apnotvar Bool) % 168.77/169.04 (declare-const tptp.pushprop_lthm_orig Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 168.77/169.04 (declare-const tptp.hoaslaminj Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3aaa Bool) % 168.77/169.04 (declare-const tptp.induction2lem_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3 Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem2 Bool) % 168.77/169.04 (declare-const tptp.termmset_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem1 Bool) % 168.77/169.04 (declare-const tptp.hoaslamnotap_lthm Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasapnotvar Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem0 Bool) % 168.77/169.04 (declare-const tptp.hoasinduction Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_gthm Bool) % 168.77/169.04 (declare-const tptp.axapp Bool) % 168.77/169.04 (declare-const tptp.hoaslamnotvar_lthm Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 168.77/169.04 (declare-const tptp.ulamvarind Bool) % 168.77/169.04 (declare-const tptp.induction Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 168.77/169.04 (declare-const tptp.termmset_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3aa Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 168.77/169.04 (declare-const tptp.hoaslamnotap_gthm Bool) % 168.77/169.04 (declare-const tptp.hoaslamnotvar_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem2v2 Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 168.77/169.04 (declare-const tptp.axclos Bool) % 168.77/169.04 (declare-const tptp.axassoc Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem2v2 Bool) % 168.77/169.04 (declare-const tptp.pushprop_lthm Bool) % 168.77/169.04 (declare-const tptp.apinj2 Bool) % 168.77/169.04 (declare-const tptp.apinj1 Bool) % 168.77/169.04 (declare-const tptp.hoasapinj2_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3v2a Bool) % 168.77/169.04 (declare-const tptp.hoasapinj1_lthm Bool) % 168.77/169.04 (declare-const tptp.hoaslaminj_lthm Bool) % 168.77/169.04 (declare-const tptp.axvarcons Bool) % 168.77/169.04 (declare-const tptp.axscons Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 168.77/169.04 (declare-const tptp.d_one tptp.d_term) % 168.77/169.04 (declare-const tptp.hoaslamnotap Bool) % 168.77/169.04 (declare-const tptp.ulamvarsh Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem3v2 Bool) % 168.77/169.04 (declare-const tptp.axshiftcons Bool) % 168.77/169.04 (declare-const tptp.id tptp.subst) % 168.77/169.04 (declare-const tptp.pushprop_lem1_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 168.77/169.04 (declare-const tptp.pushprop_lem0_lthm Bool) % 168.77/169.04 (declare-const tptp.one tptp.term) % 168.77/169.04 (declare-const tptp.substmonoid_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3v2 Bool) % 168.77/169.04 (declare-const tptp.sh tptp.subst) % 168.77/169.04 (declare-const tptp.termmset Bool) % 168.77/169.04 (declare-const tptp.induction2 Bool) % 168.77/169.04 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 168.77/169.04 (declare-const tptp.lam (-> tptp.term tptp.term)) % 168.77/169.04 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 168.77/169.04 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 168.77/169.04 (declare-const tptp.axvarid Bool) % 168.77/169.04 (declare-const tptp.d_id tptp.d_subst) % 168.77/169.04 (declare-const tptp.var (-> tptp.term Bool)) % 168.77/169.04 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 168.77/169.04 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 168.77/169.04 (declare-const tptp.hoasapnotvar_lthm Bool) % 168.77/169.04 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 168.77/169.04 (declare-const tptp.hoasinduction_lthm_3 Bool) % 168.77/169.04 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 168.77/169.04 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 168.77/169.04 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 168.77/169.04 (declare-const tptp.induction2_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3a Bool) % 168.77/169.04 (declare-const tptp.lamnotvar Bool) % 168.77/169.04 (declare-const tptp.substmonoid Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3b Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 168.77/169.04 (declare-const tptp.pushprop Bool) % 168.77/169.04 (declare-const tptp.substmonoid_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 168.77/169.04 (declare-const tptp.induction2_lthm Bool) % 168.77/169.04 (declare-const tptp.hoaslaminj_gthm Bool) % 168.77/169.04 (declare-const tptp.axidl Bool) % 168.77/169.04 (declare-const tptp.hoaslamnotvar Bool) % 168.77/169.04 (declare-const tptp.hoasapinj1_gthm Bool) % 168.77/169.04 (declare-const tptp.lamnotap Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasapinj2_gthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 168.77/169.04 (declare-const tptp.axabs Bool) % 168.77/169.04 (declare-const tptp.pushprop_gthm Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem0 Bool) % 168.77/169.04 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 168.77/169.04 (declare-const tptp.laminj Bool) % 168.77/169.04 (declare-const tptp.pushprop_lem1 Bool) % 168.77/169.04 (declare-const tptp.axidr Bool) % 168.77/169.04 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 168.77/169.04 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 168.77/169.04 (define @t3 () (_ @t2 tptp.id)) % 168.77/169.04 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 168.77/169.04 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 168.77/169.04 (define @t6 () (_ tptp.lam @t5)) % 168.77/169.04 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 168.77/169.04 (define @t8 () (@var "A" tptp.term)) % 168.77/169.04 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 168.77/169.04 (define @t10 () (not @t9)) % 168.77/169.04 (define @t11 () (@list @t8)) % 168.77/169.04 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 168.77/169.04 (define @t13 () (@var "N" tptp.subst)) % 168.77/169.04 (define @t14 () (_ tptp.sub @t8)) % 168.77/169.04 (define @t15 () (_ @t14 @t13)) % 168.77/169.04 (define @t16 () (@var "M" tptp.subst)) % 168.77/169.04 (define @t17 () (_ tptp.comp @t16)) % 168.77/169.04 (define @t18 () (_ @t17 @t13)) % 168.77/169.04 (define @t19 () (_ (_ @t4 @t16) @t8)) % 168.77/169.04 (define @t20 () (@list @t16 @t8 @t13)) % 168.77/169.04 (define @t21 () (not (forall @t20 (= (_ (_ tptp.sub @t19) @t13) (_ (_ @t4 @t18) @t15))))) % 168.77/169.04 (define @t22 () (@list @t4)) % 168.77/169.04 (define @t23 () (not (forall @t22 (or @t21 @t12 @t7)))) % 168.77/169.04 (define @t24 () (@var "B" tptp.term)) % 168.77/169.04 (define @t25 () (_ @t14 tptp.id)) % 168.77/169.04 (define @t26 () (_ tptp.ap @t25)) % 168.77/169.04 (define @t27 () (not (_ (_ @t3 @t24) tptp.id))) % 168.77/169.04 (define @t28 () (@list @t8 @t24)) % 168.77/169.04 (define @t29 () (not (forall @t28 (or @t10 @t27 (_ (_ @t3 (_ @t26 @t24)) tptp.id))))) % 168.77/169.04 (define @t30 () (@var "K" tptp.subst)) % 168.77/169.04 (define @t31 () (_ (_ tptp.comp @t30) @t13)) % 168.77/169.04 (define @t32 () (_ (_ @t2 @t16) @t8)) % 168.77/169.04 (define @t33 () (_ @t32 @t31)) % 168.77/169.04 (define @t34 () (_ @t14 @t30)) % 168.77/169.04 (define @t35 () (_ @t17 @t30)) % 168.77/169.04 (define @t36 () (_ (_ (_ @t2 @t35) @t34) @t13)) % 168.77/169.04 (define @t37 () (not @t36)) % 168.77/169.04 (define @t38 () (or @t37 @t33)) % 168.77/169.04 (define @t39 () (@list @t16 @t8 @t13 @t30)) % 168.77/169.04 (define @t40 () (forall @t39 @t38)) % 168.77/169.04 (define @t41 () (not @t40)) % 168.77/169.04 (define @t42 () (not @t33)) % 168.77/169.04 (define @t43 () (or @t42 @t36)) % 168.77/169.04 (define @t44 () (forall @t39 @t43)) % 168.77/169.04 (define @t45 () (not @t44)) % 168.77/169.04 (define @t46 () (forall (@list @t2 @t1) (or @t45 @t41 (not (forall @t11 (or (not (_ tptp.var @t25)) @t9))) @t29 @t23 (_ (_ @t3 @t1) tptp.id)))) % 168.77/169.04 (define @t47 () (@var "Bound_variable_2931" tptp.term)) % 168.77/169.04 (define @t48 () (@var "Q" (-> tptp.term Bool))) % 168.77/169.04 (define @t49 () (_ tptp.push @t24)) % 168.77/169.04 (define @t50 () (_ @t49 tptp.id)) % 168.77/169.04 (define @t51 () (not (_ @t48 @t24))) % 168.77/169.04 (define @t52 () (@list @t24)) % 168.77/169.04 (define @t53 () (@var "X" tptp.term)) % 168.77/169.04 (define @t54 () (_ @t48 @t53)) % 168.77/169.04 (define @t55 () (@list @t53)) % 168.77/169.04 (define @t56 () (forall @t55 (= @t54 (_ (_ @t3 @t53) tptp.id)))) % 168.77/169.04 (define @t57 () (not @t56)) % 168.77/169.04 (define @t58 () (forall (@list @t2 @t48 @t47) (or @t23 @t57 (not (forall @t52 (or @t51 (_ @t48 (_ (_ tptp.sub @t47) @t50))))) (_ @t48 (_ tptp.lam @t47))))) % 168.77/169.04 (define @t59 () (forall @t11 (= @t8 @t25))) % 168.77/169.04 (define @t60 () (@var "Bound_variable_2367" tptp.term)) % 168.77/169.04 (define @t61 () (@var "P" (-> tptp.term Bool))) % 168.77/169.04 (define @t62 () (_ tptp.lam @t8)) % 168.77/169.04 (define @t63 () (_ @t61 @t62)) % 168.77/169.04 (define @t64 () (not (_ @t61 @t24))) % 168.77/169.04 (define @t65 () (not (forall @t11 (or (not (forall @t52 (or @t64 (_ @t61 (_ @t14 @t50))))) @t63)))) % 168.77/169.04 (define @t66 () (_ tptp.ap @t8)) % 168.77/169.04 (define @t67 () (_ @t61 @t8)) % 168.77/169.04 (define @t68 () (not @t67)) % 168.77/169.04 (define @t69 () (not (forall @t28 (or @t68 @t64 (_ @t61 (_ @t66 @t24)))))) % 168.77/169.04 (define @t70 () (_ tptp.var @t8)) % 168.77/169.04 (define @t71 () (not @t70)) % 168.77/169.04 (define @t72 () (not (forall @t11 (or @t71 @t67)))) % 168.77/169.04 (define @t73 () (forall (@list @t61 @t60) (or @t72 @t69 @t65 (_ @t61 @t60)))) % 168.77/169.04 (define @t74 () (@list @t48)) % 168.77/169.04 (define @t75 () (@list @t2)) % 168.77/169.04 (define @t76 () (forall @t75 (not (forall @t74 @t57)))) % 168.77/169.04 (define @t77 () (@var "Bound_variable_2910" tptp.term)) % 168.77/169.04 (define @t78 () (forall (@list @t2 @t48 @t77) (or @t45 @t41 @t23 @t57 (not (forall @t52 (or @t51 (_ @t48 (_ (_ tptp.sub @t77) @t50))))) (_ @t48 (_ tptp.lam @t77))))) % 168.77/169.04 (define @t79 () (_ (_ tptp.push @t8) @t16)) % 168.77/169.04 (define @t80 () (forall @t55 (= @t54 (_ @t61 (_ (_ tptp.sub @t53) @t79))))) % 168.77/169.04 (define @t81 () (not @t80)) % 168.77/169.04 (define @t82 () (forall (@list @t61 @t8 @t16) (not (forall @t74 @t81)))) % 168.77/169.04 (define @t83 () (_ tptp.comp tptp.sh)) % 168.77/169.04 (define @t84 () (@list @t8 @t16)) % 168.77/169.04 (define @t85 () (forall @t84 (= @t16 (_ @t83 @t79)))) % 168.77/169.04 (define @t86 () (@var "K" (-> tptp.term Bool))) % 168.77/169.04 (define @t87 () (forall (@list @t61 @t86 @t8 @t16 @t24) (or @t68 (_ @t86 (_ @t14 (_ @t49 @t16)))))) % 168.77/169.04 (define @t88 () (_ tptp.sub tptp.one)) % 168.77/169.04 (define @t89 () (forall @t84 (= @t8 (_ @t88 @t79)))) % 168.77/169.04 (define @t90 () (@var "Bound_variable_2605" tptp.term)) % 168.77/169.04 (define @t91 () (@var "Bound_variable_2603" tptp.term)) % 168.77/169.04 (define @t92 () (_ tptp.d2subst tptp.d_id)) % 168.77/169.04 (define @t93 () (_ tptp.d2term tptp.d_one)) % 168.77/169.04 (define @t94 () (@var "Bound_variable_3295" tptp.term)) % 168.77/169.04 (define @t95 () (forall (@list @t2 @t94) (or @t29 @t23 (_ (_ @t3 @t94) tptp.id)))) % 168.77/169.04 (define @t96 () (@var "Bound_variable_3232" tptp.term)) % 168.77/169.04 (define @t97 () (forall (@list @t2 @t96) (or @t23 (not (forall @t52 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t96) @t50)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t96)) tptp.id)))) % 168.77/169.04 (define @t98 () (@list @t16)) % 168.77/169.04 (define @t99 () (forall @t98 (= @t16 (_ @t17 tptp.id)))) % 168.77/169.04 (define @t100 () (forall @t98 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 168.77/169.04 (define @t101 () (and @t100 @t99)) % 168.77/169.04 (define @t102 () (_ (_ tptp.push tptp.one) tptp.sh)) % 168.77/169.04 (define @t103 () (_ tptp.sub @t24)) % 168.77/169.04 (define @t104 () (forall @t52 (not (forall @t22 (not (= @t5 (_ @t103 @t102))))))) % 168.77/169.04 (define @t105 () (@var "Bound_variable_2342" tptp.subst)) % 168.77/169.04 (define @t106 () (@var "Bound_variable_2340" tptp.term)) % 168.77/169.04 (define @t107 () (forall (@list @t61 @t106 @t105) (or @t69 @t65 (not (forall @t52 (or (not (_ tptp.var @t24)) (_ @t61 (_ @t103 @t105))))) (_ @t61 (_ (_ tptp.sub @t106) @t105))))) % 168.77/169.04 (define @t108 () (forall @t52 (not (forall @t22 (not (forall @t84 (= (_ @t103 @t79) @t19))))))) % 168.77/169.04 (define @t109 () (@var "Bound_variable_3211" tptp.term)) % 168.77/169.04 (define @t110 () (forall (@list @t2 @t109) (or @t45 @t41 @t23 (not (forall @t52 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t109) @t50)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t109)) tptp.id)))) % 168.77/169.04 (define @t111 () (@var "Bound_variable_3046" tptp.term)) % 168.77/169.04 (define @t112 () (_ tptp.sub @t111)) % 168.77/169.04 (define @t113 () (forall (@list @t2 @t111) (or @t23 (not (forall @t52 (or @t27 (_ (_ @t3 (_ @t112 @t50)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t112 @t102))) tptp.id)))) % 168.77/169.04 (define @t114 () (= @t8 @t24)) % 168.77/169.04 (define @t115 () (forall @t28 (or (not (= @t62 (_ tptp.lam @t24))) @t114))) % 168.77/169.04 (define @t116 () (@var "Bound_variable_2551" tptp.term)) % 168.77/169.04 (define @t117 () (@var "Bound_variable_2549" tptp.subst)) % 168.77/169.04 (define @t118 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 168.77/169.04 (define @t119 () (forall (@list @t4 @t118 @t117 @t116) (or @t21 (not (forall @t20 (= (_ (_ tptp.sub (_ (_ @t118 @t16) @t8)) @t13) (_ (_ @t118 @t18) @t15)))) (not (= @t6 (_ tptp.lam (_ (_ @t118 tptp.sh) tptp.one)))) (= (_ (_ @t4 @t117) @t116) (_ (_ @t118 @t117) @t116))))) % 168.77/169.04 (define @t120 () (@var "D" tptp.term)) % 168.77/169.04 (define @t121 () (@var "C" tptp.term)) % 168.77/169.04 (define @t122 () (not (= (_ @t26 @t121) (_ (_ tptp.ap (_ @t103 tptp.id)) @t120)))) % 168.77/169.04 (define @t123 () (@list @t8 @t24 @t121 @t120)) % 168.77/169.04 (define @t124 () (forall @t123 (or @t122 @t114))) % 168.77/169.04 (define @t125 () (not (= (_ @t66 @t121) (_ (_ tptp.ap @t24) @t120)))) % 168.77/169.04 (define @t126 () (forall @t123 (or @t125 @t114))) % 168.77/169.04 (define @t127 () (= @t121 @t120)) % 168.77/169.04 (define @t128 () (forall @t123 (or @t122 @t127))) % 168.77/169.04 (define @t129 () (forall @t123 (or @t125 @t127))) % 168.77/169.04 (define @t130 () (@var "Bound_variable_2822" tptp.term)) % 168.77/169.04 (define @t131 () (@var "Bound_variable_2820" tptp.term)) % 168.77/169.04 (define @t132 () (@var "Bound_variable_2140" tptp.term)) % 168.77/169.04 (define @t133 () (forall (@list @t61 @t132) (or @t72 @t69 (not (forall @t11 (or @t68 @t63))) (_ @t61 @t132)))) % 168.77/169.04 (define @t134 () (forall (@list @t61 @t48 @t8 @t16) (or @t68 @t81 (_ @t48 tptp.one)))) % 168.77/169.04 (define @t135 () (@var "Bound_variable_3001" tptp.term)) % 168.77/169.04 (define @t136 () (@var "Bound_variable_2999" tptp.term)) % 168.77/169.04 (define @t137 () (forall (@list @t2 @t136 @t135) (or @t45 @t41 @t29 (not (_ (_ @t3 @t136) tptp.id)) (not (_ (_ @t3 @t135) tptp.id)) (_ (_ @t3 (_ (_ tptp.ap @t136) @t135)) tptp.id)))) % 168.77/169.04 (define @t138 () (@var "Bound_variable_3171" tptp.term)) % 168.77/169.04 (define @t139 () (_ tptp.sub @t138)) % 168.77/169.04 (define @t140 () (@var "Bound_variable_3094" tptp.subst)) % 168.77/169.04 (define @t141 () (@var "Bound_variable_3090" tptp.subst)) % 168.77/169.04 (define @t142 () (_ (_ tptp.comp @t141) @t140)) % 168.77/169.04 (define @t143 () (@var "Bound_variable_3092" tptp.term)) % 168.77/169.04 (define @t144 () (_ (_ tptp.sub @t143) @t140)) % 168.77/169.04 (define @t145 () (@var "Bound_variable_3149" tptp.term)) % 168.77/169.04 (define @t146 () (_ tptp.sub @t145)) % 168.77/169.04 (define @t147 () (@var "Bound_variable_3076" tptp.subst)) % 168.77/169.04 (define @t148 () (@var "Bound_variable_3072" tptp.subst)) % 168.77/169.04 (define @t149 () (@var "Bound_variable_3074" tptp.term)) % 168.77/169.04 (define @t150 () (not (_ tptp.var @t93))) % 168.77/169.04 (define @t151 () (@var "DS2" tptp.d_subst)) % 168.77/169.04 (define @t152 () (@var "DS1" tptp.d_subst)) % 168.77/169.04 (define @t153 () (@var "DS" tptp.d_subst)) % 168.77/169.04 (define @t154 () (@list @t153)) % 168.77/169.04 (define @t155 () (@var "S" tptp.subst)) % 168.77/169.04 (define @t156 () (@var "DT2" tptp.d_term)) % 168.77/169.04 (define @t157 () (@var "DT1" tptp.d_term)) % 168.77/169.04 (define @t158 () (@var "DT" tptp.d_term)) % 168.77/169.04 (define @t159 () (@list @t158)) % 168.77/169.04 (define @t160 () (forall @t159 (= @t158 tptp.d_one))) % 168.77/169.04 (define @t161 () (_ tptp.d2term @t158)) % 168.77/169.04 (define @t162 () (@var "T" tptp.term)) % 168.77/169.04 (define @t163 () (= @t162 @t161)) % 168.77/169.04 (define @t164 () (exists @t159 @t163)) % 168.77/169.04 (define @t165 () (@list @t162)) % 168.77/169.04 (define @t166 () (forall @t165 @t164)) % 168.77/169.04 (define @t167 () (forall @t11 (=> @t70 @t9))) % 168.77/169.04 (define @t168 () (_ (_ (_ tptp.hoasvar tptp.id) @t8) tptp.id)) % 168.77/169.04 (define @t169 () (forall @t11 (=> @t168 @t9))) % 168.77/169.04 (define @t170 () (=> @t169 @t167)) % 168.77/169.04 (define @t171 () (forall @t39 (=> @t36 @t33))) % 168.77/169.04 (define @t172 () (=> @t171 @t170)) % 168.77/169.04 (define @t173 () (forall @t39 (=> @t33 @t36))) % 168.77/169.04 (define @t174 () (=> @t173 @t172)) % 168.77/169.04 (define @t175 () (forall @t75 @t174)) % 168.77/169.04 (define @t176 () (= tptp.hoasinduction_lem1 @t175)) % 168.77/169.04 (define @t177 () (not @t176)) % 168.77/169.04 (define @t178 () (@const 0 (@ho-elim-sort (-> tptp.d_term tptp.term)))) % 168.77/169.04 (define @t179 () (@const 1 (-> (@ho-elim-sort (-> tptp.d_term tptp.term)) tptp.d_term tptp.term))) % 168.77/169.04 (define @t180 () (@const 2 (@ho-elim-sort (-> tptp.term Bool)))) % 168.77/169.04 (define @t181 () (@const 3 (-> (@ho-elim-sort (-> tptp.term Bool)) tptp.term Bool))) % 168.77/169.04 (define @t182 () (_ (@const 5 (-> (@ho-elim-sort (-> tptp.d_subst tptp.subst)) tptp.d_subst tptp.subst)) (@const 4 (@ho-elim-sort (-> tptp.d_subst tptp.subst))) tptp.d_id)) % 168.77/169.04 (define @t183 () (@var "BOUND_VARIABLE_9038" tptp.term)) % 168.77/169.04 (define @t184 () (@var "BOUND_VARIABLE_10122" (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool)))) % 168.77/169.04 (define @t185 () (@const 6 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.subst Bool))))) % 168.77/169.04 (define @t186 () (_ @t185 @t184 @t182)) % 168.77/169.04 (define @t187 () (@const 7 (-> (@ho-elim-sort (-> tptp.term tptp.subst Bool)) tptp.term (@ho-elim-sort (-> tptp.subst Bool))))) % 168.77/169.04 (define @t188 () (@const 8 (-> (@ho-elim-sort (-> tptp.subst Bool)) tptp.subst Bool))) % 168.77/169.04 (define @t189 () (not (_ @t188 (_ @t187 (_ @t185 (@const 9 (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool))) @t182) @t8) @t182))) % 168.77/169.04 (define @t190 () (@const 10 (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)))) % 168.77/169.04 (define @t191 () (@const 11 (-> (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)) tptp.subst (@ho-elim-sort (-> tptp.subst tptp.subst))))) % 168.77/169.04 (define @t192 () (@const 12 (-> (@ho-elim-sort (-> tptp.subst tptp.subst)) tptp.subst tptp.subst))) % 168.77/169.04 (define @t193 () (_ @t192 (_ @t191 @t190 @t30) @t13)) % 168.77/169.04 (define @t194 () (_ @t188 (_ @t187 (_ @t185 @t184 @t16) @t8) @t193)) % 168.77/169.04 (define @t195 () (_ (@const 15 (-> (@ho-elim-sort (-> tptp.subst tptp.term)) tptp.subst tptp.term)) (_ (@const 14 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term)))) (@const 13 (@ho-elim-sort (-> tptp.term tptp.subst tptp.term))) @t8) @t30)) % 168.77/169.04 (define @t196 () (_ @t192 (_ @t191 @t190 @t16) @t30)) % 168.77/169.04 (define @t197 () (_ @t188 (_ @t187 (_ @t185 @t184 @t196) @t195) @t13)) % 168.77/169.04 (define @t198 () (forall (@list @t184 @t183) (or (not (forall @t39 (or (not @t194) @t197))) (not (forall @t39 (or (not @t197) @t194))) (not (forall @t11 (or @t189 (_ @t188 (_ @t187 @t186 @t8) @t182)))) (not (_ @t181 @t180 @t183)) (_ @t188 (_ @t187 @t186 @t183) @t182)))) % 168.77/169.04 (define @t199 () (@quantifiers_skolemize @t198 1)) % 168.77/169.04 (define @t200 () (_ @t179 @t178 @t158)) % 168.77/169.04 (define @t201 () (forall @t159 (not (= @t200 @t199)))) % 168.77/169.04 (define @t202 () (@quantifiers_skolemize @t201 0)) % 168.77/169.04 (define @t203 () (_ @t179 @t178 @t202)) % 168.77/169.04 (define @t204 () (forall @t165 (not (forall @t159 (not (= @t162 @t200)))))) % 168.77/169.04 (define @t205 () (tptp.d2term @t158)) % 168.77/169.04 (define @t206 () (not @t163)) % 168.77/169.04 (define @t207 () (forall @t159 @t206)) % 168.77/169.04 (define @t208 () (not @t207)) % 168.77/169.04 (define @t209 () (not (= @t199 @t200))) % 168.77/169.04 (define @t210 () (forall @t159 @t209)) % 168.77/169.04 (define @t211 () (not @t210)) % 168.77/169.04 (define @t212 () (not @t201)) % 168.77/169.04 (define @t213 () (= @t199 @t203)) % 168.77/169.04 (define @t214 () (= @t203 @t199)) % 168.77/169.04 (define @t215 () (not (not @t214))) % 168.77/169.04 (define @t216 () (@list true)) % 168.77/169.04 (define @t217 () (_ @t181 @t180 @t199)) % 168.77/169.04 (define @t218 () (tptp.d2subst tptp.d_id)) % 168.77/169.04 (define @t219 () (not (tptp.var @t183))) % 168.77/169.04 (define @t220 () (not (forall @t11 (or (not (tptp.hoasvar @t218 @t8 @t218)) (_ @t2 @t218 @t8 @t218))))) % 168.77/169.04 (define @t221 () (tptp.comp @t30 @t13)) % 168.77/169.04 (define @t222 () (_ @t2 @t16 @t8 @t221)) % 168.77/169.04 (define @t223 () (tptp.sub @t8 @t30)) % 168.77/169.04 (define @t224 () (tptp.comp @t16 @t30)) % 168.77/169.04 (define @t225 () (_ @t2 @t224 @t223 @t13)) % 168.77/169.04 (define @t226 () (forall @t39 (or (not @t225) @t222))) % 168.77/169.04 (define @t227 () (not @t226)) % 168.77/169.04 (define @t228 () (forall @t39 (or (not @t222) @t225))) % 168.77/169.04 (define @t229 () (not @t228)) % 168.77/169.04 (define @t230 () (@list @t2 @t183)) % 168.77/169.04 (define @t231 () (_ @t2 @t92 @t183 @t92)) % 168.77/169.04 (define @t232 () (or @t229 @t227 @t220 @t219 @t231)) % 168.77/169.04 (define @t233 () (_ @t2 @t92 @t8 @t92)) % 168.77/169.04 (define @t234 () (tptp.hoasvar @t92 @t8 @t92)) % 168.77/169.04 (define @t235 () (not @t234)) % 168.77/169.04 (define @t236 () (or @t235 @t233)) % 168.77/169.04 (define @t237 () (forall @t11 @t236)) % 168.77/169.04 (define @t238 () (not @t237)) % 168.77/169.04 (define @t239 () (or @t229 @t227 @t238 @t219 @t231)) % 168.77/169.04 (define @t240 () (forall @t230 @t239)) % 168.77/169.04 (define @t241 () (_ @t2 tptp.id @t183 tptp.id)) % 168.77/169.04 (define @t242 () (_ @t2 tptp.id @t8 tptp.id)) % 168.77/169.04 (define @t243 () (tptp.hoasvar tptp.id @t8 tptp.id)) % 168.77/169.04 (define @t244 () (not @t243)) % 168.77/169.04 (define @t245 () (or @t244 @t242)) % 168.77/169.04 (define @t246 () (forall @t11 @t245)) % 168.77/169.04 (define @t247 () (not @t246)) % 168.77/169.04 (define @t248 () (or @t229 @t227 @t247 @t219 @t241)) % 168.77/169.04 (define @t249 () (forall @t230 @t248)) % 168.77/169.04 (define @t250 () (= tptp.hoasinduction_lem1 @t249)) % 168.77/169.04 (define @t251 () (or @t219 @t241)) % 168.77/169.04 (define @t252 () (or @t229 @t227 @t247 @t251)) % 168.77/169.04 (define @t253 () (forall @t230 @t252)) % 168.77/169.04 (define @t254 () (@list @t183)) % 168.77/169.04 (define @t255 () (forall @t254 @t252)) % 168.77/169.04 (define @t256 () (forall @t254 @t251)) % 168.77/169.04 (define @t257 () (or @t229 @t227 @t247 @t256)) % 168.77/169.04 (define @t258 () (tptp.var @t8)) % 168.77/169.04 (define @t259 () (forall @t11 (or (not @t258) @t242))) % 168.77/169.04 (define @t260 () (or @t229 @t227 @t247 @t259)) % 168.77/169.04 (define @t261 () (or @t227 @t247 @t259)) % 168.77/169.04 (define @t262 () (=> @t246 @t259)) % 168.77/169.04 (define @t263 () (=> @t226 @t262)) % 168.77/169.04 (define @t264 () (or @t71 @t9)) % 168.77/169.04 (define @t265 () (not @t168)) % 168.77/169.04 (define @t266 () (or @t265 @t9)) % 168.77/169.04 (define @t267 () (@quantifiers_skolemize @t198 0)) % 168.77/169.04 (define @t268 () (_ @t185 @t267 @t182)) % 168.77/169.04 (define @t269 () (not @t217)) % 168.77/169.04 (define @t270 () (_ @t188 (_ @t187 (_ @t185 @t267 @t16) @t8) @t193)) % 168.77/169.04 (define @t271 () (_ @t188 (_ @t187 (_ @t185 @t267 @t196) @t195) @t13)) % 168.77/169.04 (define @t272 () (or (not (forall @t39 (or (not @t270) @t271))) (not (forall @t39 (or (not @t271) @t270))) (not (forall @t11 (or @t189 (_ @t188 (_ @t187 @t268 @t8) @t182)))) @t269 (_ @t188 (_ @t187 @t268 @t199) @t182))) % 168.77/169.04 (assume @p1 (and @t166 @t160 (forall (@list @t157 @t156) (=> (= (_ tptp.d2term @t157) (_ tptp.d2term @t156)) (= @t157 @t156))) (forall (@list @t155) (exists @t154 (= @t155 (_ tptp.d2subst @t153)))) (forall @t154 (= @t153 tptp.d_id)) (forall (@list @t152 @t151) (=> (= (_ tptp.d2subst @t152) (_ tptp.d2subst @t151)) (= @t152 @t151))) (= tptp.one @t93) (= (_ (_ tptp.ap @t93) @t93) @t93) (= (_ tptp.lam @t93) @t93) (= (_ (_ tptp.sub @t93) @t92) @t93) (= tptp.id @t92) (= tptp.sh @t92) (= (_ (_ tptp.push @t93) @t92) @t92) (= (_ (_ tptp.comp @t92) @t92) @t92) (= (_ (_ (_ (_ tptp.hoasap @t92) @t93) @t92) @t93) @t93) (= tptp.hoaslam (lambda (@list (@var "Bound_variable_4913" tptp.subst) (@var "Bound_variable_4915" (-> tptp.subst tptp.term tptp.term))) @t93)) (= tptp.hoasinduction_p_and_p_prime (lambda (@list @t2 @t48) @t56)) (= tptp.pushprop_p_and_p_prime (lambda (@list @t8 @t16 @t61 @t48) @t80)) @t150 (= tptp.pushprop_lem1v2 @t134) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t28 (or (not (= (_ @t14 tptp.sh) (_ @t103 tptp.sh))) @t114))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t107) (= tptp.hoasinduction_lem3v2_f @t108) tptp.axvarshift (= tptp.hoasapinj2 @t128) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t124) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t89 (=> @t85 (=> @t99 (=> @t133 @t107))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t108) (= tptp.hoasinduction_lthm (=> @t73 (=> @t137 (=> @t110 @t46)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t76 (=> @t73 (=> @t59 (=> @t58 @t95))))) (= tptp.hoaslaminj @t119) (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t138) (or (not (forall (@list @t4 @t145) (or @t12 @t7 (not (forall (@list @t148 @t149 @t147) (= (_ (_ tptp.sub (_ (_ @t4 @t148) @t149)) @t147) (_ (_ tptp.sub (_ @t146 (_ (_ tptp.push @t149) @t148))) @t147)))) (not (forall (@list @t141 @t143 @t140) (= (_ (_ @t4 @t142) @t144) (_ @t146 (_ (_ tptp.push @t144) @t142)))))))) (not (forall @t52 (or @t27 (_ (_ @t3 (_ @t139 @t50)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t139 @t102))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t113) (= tptp.hoasinduction_lem3 @t110) (= tptp.hoasinduction_lem2 @t137) (= tptp.termmset_lthm (=> @t59 @t59)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t89 @t134)) tptp.hoasapnotvar (= tptp.hoasinduction_lem0 @t76) (= tptp.hoasinduction @t46) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t104) tptp.ulamvarind (= tptp.induction @t133) (= tptp.hoasinduction_lem3a_lthm (=> @t59 (=> @t113 @t97))) tptp.termmset_gthm (= tptp.hoasinduction_lem3aa @t113) 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 (= tptp.hoasinduction_lem2v2 (forall (@list @t2 @t48 @t131 @t130) (or @t45 @t41 @t29 @t57 (not (_ @t48 @t131)) (not (_ @t48 @t130)) (_ @t48 (_ (_ tptp.ap @t131) @t130))))) tptp.pushprop_lthm (= tptp.apinj2 @t129) (= tptp.apinj1 @t126) (= tptp.hoasapinj2_lthm (=> @t129 @t128)) (= tptp.hoasinduction_lem3v2a @t58) (= tptp.hoasapinj1_lthm (=> @t59 (=> @t126 @t124))) (= tptp.hoaslaminj_lthm (=> @t89 (=> @t85 (=> @t115 @t119)))) (= tptp.axvarcons @t89) (= tptp.axscons (forall @t98 (= @t16 (_ (_ tptp.push (_ @t88 @t16)) (_ @t83 @t16))))) tptp.hoasinduction_lem2v2_gthm (= tptp.axidr @t99) (= tptp.pushprop_lem1 @t87) (= tptp.laminj @t115) (= tptp.hoasinduction_lem3_lthm (=> @t59 (=> @t113 @t110))) (= tptp.pushprop_lem0 @t82) tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t108 (=> @t59 @t58))) tptp.hoasinduction_lem2_lthm tptp.hoasapinj2_gthm tptp.hoasinduction_lem1_lthm (not tptp.lamnotap) tptp.hoasapinj1_gthm tptp.hoaslamnotvar (= tptp.axidl @t100) tptp.hoaslaminj_gthm (= tptp.induction2_lthm (=> @t59 (=> @t107 @t73))) (= tptp.hoasinduction_lem0_lthm @t76) (= tptp.substmonoid_lthm (=> @t100 (=> @t99 @t101))) tptp.pushprop tptp.hoasinduction_lem3_gthm tptp.hoasinduction_lem2_gthm (= tptp.hoasinduction_lem3b @t104) (= tptp.substmonoid @t101) tptp.lamnotvar (= tptp.hoasinduction_lem3a @t97) tptp.hoasinduction_lem1_gthm (= tptp.hoasinduction_no_psi_cond @t95) tptp.induction2_gthm tptp.pushprop_lem2v2_lthm (not (_ (_ (_ tptp.hoasvar @t92) @t93) @t92)) (= tptp.hoaslamnotap (forall (@list @t4 @t91 @t90) (or @t21 (not (= @t6 (_ (_ tptp.ap (_ (_ tptp.sub @t91) tptp.id)) @t90)))))) tptp.substmonoid_gthm tptp.ulamvarsh (= tptp.induction2 @t73) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t89 (=> @t85 @t87))) (= tptp.hoasinduction_lem3v2 @t78) (= tptp.axshiftcons @t85) (= tptp.termmset @t59) (= tptp.pushprop_lem0_lthm @t82) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t59 @t78)) (= tptp.axvarid @t59) (= tptp.hoasinduction_lthm_3 (=> @t76 (=> @t73 (=> @t59 (=> @t58 @t46))))))) % 168.77/169.04 (assume @p2 @t177) % 168.77/169.04 (assume @p3 true) % 168.77/169.04 (step @p4 :rule evaluate :args ((= true false))) % 168.77/169.04 ; WARNING: add trust step for TRUST % 168.77/169.04 ; trust TRUST PREPROCESS_HO_ELIM % 168.77/169.04 (step @p5 :rule trust :premises () :args ((= @t150 (not (_ @t181 @t180 (_ @t179 @t178 tptp.d_one)))))) % 168.77/169.04 (step @p6 :rule and_elim :premises (@p1) :args (18)) % 168.77/169.04 (step @p7 :rule eq_resolve :premises (@p6 @p5)) % 168.77/169.04 (step @p8 :rule false_intro :premises (@p7)) % 168.77/169.04 (step @p9 :rule eq-symm :args (@t158 tptp.d_one)) % 168.77/169.04 (step @p10 :rule cong :premises (@p9) :args (@t160)) % 168.77/169.04 (step @p11 :rule and_elim :premises (@p1) :args (1)) % 168.77/169.04 (step @p12 :rule eq_resolve :premises (@p11 @p10)) % 168.77/169.04 (step @p13 :rule instantiate :premises (@p12) :args ((@list @t202))) % 168.77/169.04 (step @p14 :rule symm :premises (@p13)) % 168.77/169.04 (step @p15 :rule refl :args (@t178)) % 168.77/169.04 (step @p16 :rule cong :premises (@p15 @p14) :args (@t203)) % 168.77/169.04 ; trust TRUST PREPROCESS_HO_ELIM % 168.77/169.04 (step @p17 :rule trust :premises () :args ((= (forall @t165 (not (forall @t159 (not (= @t162 @t205))))) @t204))) % 168.77/169.04 (step @p18 :rule refl :args (@t205)) % 168.77/169.04 (step @p19 :rule refl :args (@t161)) % 168.77/169.04 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t161 @t205))) % 168.77/169.04 (step @p21 :rule symm :premises (@p20)) % 168.77/169.04 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 168.77/169.04 (step @p23 :rule refl :args (@t162)) % 168.77/169.04 (step @p24 :rule cong :premises (@p23 @p22) :args (@t163)) % 168.77/169.04 (step @p25 :rule cong :premises (@p24) :args (@t206)) % 168.77/169.04 (step @p26 :rule cong :premises (@p25) :args (@t207)) % 168.77/169.04 (step @p27 :rule cong :premises (@p26) :args (@t208)) % 168.77/169.04 (step @p28 :rule exists-elim :args ((= @t164 @t208))) % 168.77/169.04 (step @p29 :rule trans :premises (@p28 @p27)) % 168.77/169.04 (step @p30 :rule cong :premises (@p29) :args (@t166)) % 168.77/169.04 (step @p31 :rule trans :premises (@p30 @p17)) % 168.77/169.04 (step @p32 :rule and_elim :premises (@p1) :args (0)) % 168.77/169.04 (step @p33 :rule eq_resolve :premises (@p32 @p31)) % 168.77/169.04 (step @p34 :rule eq-symm :args (@t199 @t200)) % 168.77/169.04 (step @p35 :rule cong :premises (@p34) :args (@t209)) % 168.77/169.04 (step @p36 :rule cong :premises (@p35) :args (@t210)) % 168.77/169.04 (step @p37 :rule cong :premises (@p36) :args (@t211)) % 168.77/169.04 (step @p38 :rule refl :args (@t204)) % 168.77/169.04 (step @p39 :rule cong :premises (@p38 @p37) :args ((=> @t204 @t211))) % 168.77/169.04 (assume-push @p247 @t204) % 168.77/169.04 (step @p41 :rule instantiate :premises (@p33) :args ((@list @t199))) % 168.77/169.04 (step-pop @p248 :rule scope :premises (@p41)) % 168.77/169.04 (step @p42 :rule process_scope :premises (@p248) :args (@t211)) % 168.77/169.04 (step @p44 :rule eq_resolve :premises (@p42 @p39)) % 168.77/169.04 (step @p45 :rule implies_elim :premises (@p44)) % 168.77/169.04 (step @p46 :rule chain_m_resolution :premises (@p45 @p33) :args (@t212 (@list false) (@list @t204))) % 168.77/169.04 (step @p47 :rule refl :args (@t213)) % 168.77/169.04 (step @p48 :rule bool-double-not-elim :args (@t201)) % 168.77/169.04 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or (not @t212) @t213))) % 168.77/169.04 (step @p50 :rule eq-symm :args (@t203 @t199)) % 168.77/169.04 (step @p51 :rule bool-double-not-elim :args (@t214)) % 168.77/169.04 (step @p52 :rule trans :premises (@p51 @p50)) % 168.77/169.04 (step @p53 :rule refl :args (@t212)) % 168.77/169.04 (step @p54 :rule cong :premises (@p53 @p52) :args ((=> @t212 @t215))) % 168.77/169.04 (assume-push @p249 @t212) % 168.77/169.04 (step @p56 :rule skolemize :premises (@p46)) % 168.77/169.04 (step-pop @p250 :rule scope :premises (@p56)) % 168.77/169.04 (step @p57 :rule process_scope :premises (@p250) :args (@t215)) % 168.77/169.04 (step @p59 :rule eq_resolve :premises (@p57 @p54)) % 168.77/169.04 (step @p60 :rule implies_elim :premises (@p59)) % 168.77/169.04 (step @p61 :rule eq_resolve :premises (@p60 @p49)) % 168.77/169.04 (step @p62 :rule chain_m_resolution :premises (@p61 @p46) :args (@t213 @t216 (@list @t201))) % 168.77/169.04 (step @p63 :rule trans :premises (@p62 @p16)) % 168.77/169.04 (step @p64 :rule refl :args (@t180)) % 168.77/169.04 (step @p65 :rule cong :premises (@p64 @p63) :args (@t217)) % 168.77/169.04 ; trust TRUST PREPROCESS_HO_ELIM % 168.77/169.04 (step @p66 :rule trust :premises () :args ((= (not (forall @t230 (or @t229 @t227 @t220 @t219 (_ @t2 @t218 @t183 @t218)))) (not @t198)))) % 168.77/169.04 (step @p67 :rule refl :args (@t218)) % 168.77/169.04 (step @p68 :rule refl :args (@t92)) % 168.77/169.04 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t92 @t218))) % 168.77/169.04 (step @p70 :rule symm :premises (@p69)) % 168.77/169.04 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 168.77/169.04 (step @p72 :rule refl :args (@t183)) % 168.77/169.04 (step @p73 :rule cong :premises (@p71 @p72 @p71) :args (@t231)) % 168.77/169.04 (step @p74 :rule refl :args (@t219)) % 168.77/169.04 (step @p75 :rule refl :args (@t220)) % 168.77/169.04 (step @p76 :rule refl :args (@t227)) % 168.77/169.04 (step @p77 :rule refl :args (@t229)) % 168.77/169.04 (step @p78 :rule nary_cong :premises (@p77 @p76 @p75 @p74 @p73) :args (@t232)) % 168.77/169.04 (step @p79 :rule cong :premises (@p78) :args ((forall @t230 @t232))) % 168.77/169.04 (step @p80 :rule refl :args (@t231)) % 168.77/169.04 (step @p81 :rule refl :args (@t219)) % 168.77/169.04 (step @p82 :rule refl :args (@t8)) % 168.77/169.04 (step @p83 :rule cong :premises (@p71 @p82 @p71) :args (@t233)) % 168.77/169.04 (step @p84 :rule cong :premises (@p71 @p82 @p71) :args (@t234)) % 168.77/169.04 (step @p85 :rule cong :premises (@p84) :args (@t235)) % 168.77/169.04 (step @p86 :rule nary_cong :premises (@p85 @p83) :args (@t236)) % 168.77/169.04 (step @p87 :rule cong :premises (@p86) :args (@t237)) % 168.77/169.04 (step @p88 :rule cong :premises (@p87) :args (@t238)) % 168.77/169.04 (step @p89 :rule refl :args (@t227)) % 168.77/169.04 (step @p90 :rule refl :args (@t229)) % 168.77/169.04 (step @p91 :rule nary_cong :premises (@p90 @p89 @p88 @p81 @p80) :args (@t239)) % 168.77/169.04 (step @p92 :rule cong :premises (@p91) :args (@t240)) % 168.77/169.04 (step @p93 :rule trans :premises (@p92 @p79)) % 168.77/169.04 (step @p94 :rule bool-eq-true :args (@t240)) % 168.77/169.04 (step @p95 :rule eq-symm :args (true @t240)) % 168.77/169.04 (step @p96 :rule trans :premises (@p95 @p94)) % 168.77/169.04 (step @p97 :rule trans :premises (@p96 @p93)) % 168.77/169.04 (step @p98 :rule cong :premises (@p97) :args ((not (= true @t240)))) % 168.77/169.04 (step @p99 :rule and_elim :premises (@p1) :args (10)) % 168.77/169.04 (step @p100 :rule refl :args (@t183)) % 168.77/169.04 (step @p101 :rule cong :premises (@p99 @p100 @p99) :args (@t241)) % 168.77/169.04 (step @p102 :rule refl :args (@t8)) % 168.77/169.04 (step @p103 :rule cong :premises (@p99 @p102 @p99) :args (@t242)) % 168.77/169.04 (step @p104 :rule cong :premises (@p99 @p102 @p99) :args (@t243)) % 168.77/169.04 (step @p105 :rule cong :premises (@p104) :args (@t244)) % 168.77/169.04 (step @p106 :rule nary_cong :premises (@p105 @p103) :args (@t245)) % 168.77/169.04 (step @p107 :rule cong :premises (@p106) :args (@t246)) % 168.77/169.04 (step @p108 :rule cong :premises (@p107) :args (@t247)) % 168.77/169.04 (step @p109 :rule nary_cong :premises (@p90 @p89 @p108 @p81 @p101) :args (@t248)) % 168.77/169.04 (step @p110 :rule cong :premises (@p109) :args (@t249)) % 168.77/169.04 (step @p111 :rule bool-eq-true :args (tptp.hoasinduction_lem1)) % 168.77/169.04 (step @p112 :rule symm :premises (@p111)) % 168.77/169.04 (step @p113 :rule and_elim :premises (@p1) :args (47)) % 168.77/169.04 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 168.77/169.04 (step @p115 :rule cong :premises (@p114 @p110) :args (@t250)) % 168.77/169.04 (step @p116 :rule cong :premises (@p115) :args ((not @t250))) % 168.77/169.04 (step @p117 :rule trans :premises (@p116 @p98)) % 168.77/169.04 (step @p118 :rule aci_norm :args ((= @t252 @t248))) % 168.77/169.04 (step @p119 :rule cong :premises (@p118) :args (@t253)) % 168.77/169.04 (step @p120 :rule quant-merge-prenex :args ((= (forall @t75 @t255) @t253))) % 168.77/169.04 (step @p121 :rule alpha_equiv :args (@t256 (@list @t183) (@list @t8))) % 168.77/169.04 (step @p122 :rule refl :args (@t247)) % 168.77/169.04 (step @p123 :rule nary_cong :premises (@p77 @p76 @p122 @p121) :args (@t257)) % 168.77/169.04 (step @p124 :rule quant-miniscope-or :args ((= @t255 @t257))) % 168.77/169.04 (step @p125 :rule trans :premises (@p124 @p123)) % 168.77/169.04 (step @p126 :rule symm :premises (@p125)) % 168.77/169.04 (step @p127 :rule cong :premises (@p126) :args ((forall @t75 @t260))) % 168.77/169.04 (step @p128 :rule trans :premises (@p127 @p120)) % 168.77/169.04 (step @p129 :rule trans :premises (@p128 @p119)) % 168.77/169.04 (step @p130 :rule aci_norm :args ((= (or @t229 @t261) @t260))) % 168.77/169.04 (step @p131 :rule aci_norm :args ((= (or @t227 (or @t247 @t259)) @t261))) % 168.77/169.04 (step @p132 :rule bool-impl-elim :args (@t246 @t259)) % 168.77/169.04 (step @p133 :rule nary_cong :premises (@p76 @p132) :args ((or @t227 @t262))) % 168.77/169.04 (step @p134 :rule trans :premises (@p133 @p131)) % 168.77/169.04 (step @p135 :rule bool-impl-elim :args (@t226 @t262)) % 168.77/169.04 (step @p136 :rule trans :premises (@p135 @p134)) % 168.77/169.04 (step @p137 :rule nary_cong :premises (@p77 @p136) :args ((or @t229 @t263))) % 168.77/169.04 (step @p138 :rule trans :premises (@p137 @p130)) % 168.77/169.04 (step @p139 :rule bool-impl-elim :args (@t228 @t263)) % 168.77/169.04 (step @p140 :rule trans :premises (@p139 @p138)) % 168.77/169.04 (step @p141 :rule cong :premises (@p140) :args ((forall @t75 (=> @t228 @t263)))) % 168.77/169.04 (step @p142 :rule trans :premises (@p141 @p129)) % 168.77/169.04 (step @p143 :rule refl :args (@t242)) % 168.77/169.04 (step @p144 :rule refl :args (@t9)) % 168.77/169.04 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t9 @t242))) % 168.77/169.04 (step @p146 :rule symm :premises (@p145)) % 168.77/169.04 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 168.77/169.04 (step @p148 :rule refl :args (@t258)) % 168.77/169.04 (step @p149 :rule refl :args (@t70)) % 168.77/169.04 (step @p150 :rule cong :premises (@p149 @p148) :args ((= @t70 @t258))) % 168.77/169.04 (step @p151 :rule symm :premises (@p150)) % 168.77/169.04 (step @p152 :rule eq_resolve :premises (@p149 @p151)) % 168.77/169.04 (step @p153 :rule cong :premises (@p152) :args (@t71)) % 168.77/169.04 (step @p154 :rule nary_cong :premises (@p153 @p147) :args (@t264)) % 168.77/169.04 (step @p155 :rule cong :premises (@p154) :args ((forall @t11 @t264))) % 168.77/169.04 (step @p156 :rule bool-impl-elim :args (@t70 @t9)) % 168.77/169.04 (step @p157 :rule cong :premises (@p156) :args (@t167)) % 168.77/169.04 (step @p158 :rule trans :premises (@p157 @p155)) % 168.77/169.04 (step @p159 :rule refl :args (@t243)) % 168.77/169.04 (step @p160 :rule refl :args (@t168)) % 168.77/169.04 (step @p161 :rule cong :premises (@p160 @p159) :args ((= @t168 @t243))) % 168.77/169.04 (step @p162 :rule symm :premises (@p161)) % 168.77/169.04 (step @p163 :rule eq_resolve :premises (@p160 @p162)) % 168.77/169.04 (step @p164 :rule cong :premises (@p163) :args (@t265)) % 168.77/169.04 (step @p165 :rule nary_cong :premises (@p164 @p147) :args (@t266)) % 168.77/169.04 (step @p166 :rule cong :premises (@p165) :args ((forall @t11 @t266))) % 168.77/169.04 (step @p167 :rule bool-impl-elim :args (@t168 @t9)) % 168.77/169.04 (step @p168 :rule cong :premises (@p167) :args (@t169)) % 168.77/169.04 (step @p169 :rule trans :premises (@p168 @p166)) % 168.77/169.04 (step @p170 :rule cong :premises (@p169 @p158) :args (@t170)) % 168.77/169.04 (step @p171 :rule refl :args ((_ @t2 @t16 @t8 @t31))) % 168.77/169.04 (step @p172 :rule refl :args (@t221)) % 168.77/169.04 (step @p173 :rule refl :args (@t16)) % 168.77/169.04 (step @p174 :rule cong :premises (@p173 @p82 @p172) :args (@t222)) % 168.77/169.04 (step @p175 :rule trans :premises (@p174 @p171)) % 168.77/169.04 (step @p176 :rule refl :args (@t32)) % 168.77/169.04 (step @p177 :rule ho_cong :premises (@p176 @p172)) % 168.77/169.04 (step @p178 :rule cong :premises (@p177 @p175) :args ((= (_ @t32 @t221) @t222))) % 168.77/169.04 (step @p179 :rule symm :premises (@p178)) % 168.77/169.04 (step @p180 :rule refl :args (@t33)) % 168.77/169.04 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 168.77/169.04 (step @p182 :rule refl :args (@t31)) % 168.77/169.04 (step @p183 :rule cong :premises (@p182 @p172) :args ((= @t31 @t221))) % 168.77/169.04 (step @p184 :rule symm :premises (@p183)) % 168.77/169.04 (step @p185 :rule eq_resolve :premises (@p182 @p184)) % 168.77/169.04 (step @p186 :rule ho_cong :premises (@p176 @p185)) % 168.77/169.04 (step @p187 :rule trans :premises (@p186 @p181)) % 168.77/169.04 (step @p188 :rule refl :args ((_ @t2 @t35 @t34 @t13))) % 168.77/169.04 (step @p189 :rule refl :args (@t13)) % 168.77/169.04 (step @p190 :rule refl :args (@t223)) % 168.77/169.04 (step @p191 :rule refl :args (@t224)) % 168.77/169.04 (step @p192 :rule cong :premises (@p191 @p190 @p189) :args (@t225)) % 168.77/169.04 (step @p193 :rule trans :premises (@p192 @p188)) % 168.77/169.04 (step @p194 :rule refl :args (@t2)) % 168.77/169.04 (step @p195 :rule ho_cong :premises (@p194 @p191)) % 168.77/169.04 (step @p196 :rule ho_cong :premises (@p195 @p190)) % 168.77/169.04 (step @p197 :rule ho_cong :premises (@p196 @p189)) % 168.77/169.04 (step @p198 :rule cong :premises (@p197 @p193) :args ((= (_ (_ (_ @t2 @t224) @t223) @t13) @t225))) % 168.77/169.04 (step @p199 :rule symm :premises (@p198)) % 168.77/169.04 (step @p200 :rule refl :args (@t36)) % 168.77/169.04 (step @p201 :rule eq_resolve :premises (@p200 @p199)) % 168.77/169.04 (step @p202 :rule refl :args (@t34)) % 168.77/169.04 (step @p203 :rule cong :premises (@p202 @p190) :args ((= @t34 @t223))) % 168.77/169.04 (step @p204 :rule symm :premises (@p203)) % 168.77/169.04 (step @p205 :rule eq_resolve :premises (@p202 @p204)) % 168.77/169.04 (step @p206 :rule refl :args (@t35)) % 168.77/169.04 (step @p207 :rule cong :premises (@p206 @p191) :args ((= @t35 @t224))) % 168.77/169.04 (step @p208 :rule symm :premises (@p207)) % 168.77/169.04 (step @p209 :rule eq_resolve :premises (@p206 @p208)) % 168.77/169.04 (step @p210 :rule ho_cong :premises (@p194 @p209)) % 168.77/169.04 (step @p211 :rule ho_cong :premises (@p210 @p205)) % 168.77/169.04 (step @p212 :rule ho_cong :premises (@p211 @p189)) % 168.77/169.04 (step @p213 :rule trans :premises (@p212 @p201)) % 168.77/169.04 (step @p214 :rule cong :premises (@p213) :args (@t37)) % 168.77/169.04 (step @p215 :rule nary_cong :premises (@p214 @p187) :args (@t38)) % 168.77/169.04 (step @p216 :rule cong :premises (@p215) :args (@t40)) % 168.77/169.04 (step @p217 :rule bool-impl-elim :args (@t36 @t33)) % 168.77/169.04 (step @p218 :rule cong :premises (@p217) :args (@t171)) % 168.77/169.04 (step @p219 :rule trans :premises (@p218 @p216)) % 168.77/169.04 (step @p220 :rule cong :premises (@p219 @p170) :args (@t172)) % 168.77/169.04 (step @p221 :rule cong :premises (@p187) :args (@t42)) % 168.77/169.04 (step @p222 :rule nary_cong :premises (@p221 @p213) :args (@t43)) % 168.77/169.04 (step @p223 :rule cong :premises (@p222) :args (@t44)) % 168.77/169.04 (step @p224 :rule bool-impl-elim :args (@t33 @t36)) % 168.77/169.04 (step @p225 :rule cong :premises (@p224) :args (@t173)) % 168.77/169.04 (step @p226 :rule trans :premises (@p225 @p223)) % 168.77/169.04 (step @p227 :rule cong :premises (@p226 @p220) :args (@t174)) % 168.77/169.04 (step @p228 :rule cong :premises (@p227) :args (@t175)) % 168.77/169.04 (step @p229 :rule trans :premises (@p228 @p142)) % 168.77/169.04 (step @p230 :rule refl :args (tptp.hoasinduction_lem1)) % 168.77/169.04 (step @p231 :rule cong :premises (@p230 @p229) :args (@t176)) % 168.77/169.04 (step @p232 :rule cong :premises (@p231) :args (@t177)) % 168.77/169.04 (step @p233 :rule trans :premises (@p232 @p117 @p66)) % 168.77/169.04 (step @p234 :rule eq_resolve :premises (@p2 @p233)) % 168.77/169.04 (step @p235 :rule skolemize :premises (@p234)) % 168.77/169.04 (step @p236 :rule bool-double-not-elim :args (@t217)) % 168.77/169.04 (step @p237 :rule refl :args (@t272)) % 168.77/169.04 (step @p238 :rule nary_cong :premises (@p237 @p236) :args ((or @t272 (not @t269)))) % 168.77/169.04 (step @p239 :rule cnf_or_neg :args (@t272 3)) % 168.77/169.04 (step @p240 :rule eq_resolve :premises (@p239 @p238)) % 168.77/169.04 (step @p241 :rule reordering :premises (@p240) :args ((or @t217 @t272))) % 168.77/169.04 (step @p242 :rule chain_m_resolution :premises (@p241 @p235) :args (@t217 @t216 (@list @t272))) % 168.77/169.04 (step @p243 :rule true_intro :premises (@p242)) % 168.77/169.04 (step @p244 :rule symm :premises (@p243)) % 168.77/169.04 (step @p245 :rule trans :premises (@p244 @p65 @p8)) % 168.77/169.04 (step @p246 false :rule eq_resolve :premises (@p245 @p4)) % 168.77/169.04 ) % 168.77/169.04 % SZS output end Proof % 168.77/169.04 % cvc5 exiting %------------------------------------------------------------------------------