%------------------------------------------------------------------------------ % 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 0.15s 0.42s % Output : Proof 0.15s % 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 23:02:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.36 %----Proving TH0 % 0.15/0.42 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.15/0.42 % SZS status Theorem % 0.15/0.42 % SZS output start Proof % 0.15/0.42 ( % 0.15/0.42 (declare-sort tptp.term 0) % 0.15/0.42 (declare-sort tptp.subst 0) % 0.15/0.42 (declare-sort tptp.d_term 0) % 0.15/0.42 (declare-sort tptp.d_subst 0) % 0.15/0.42 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 0.15/0.42 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 0.15/0.42 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 0.15/0.42 (declare-const tptp.pushprop_lem1v2 Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.15/0.42 (declare-const tptp.axmap Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.15/0.42 (declare-const tptp.shinj Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.15/0.42 (declare-const tptp.induction2lem Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.15/0.42 (declare-const tptp.axvarshift Bool) % 0.15/0.42 (declare-const tptp.hoasapinj2 Bool) % 0.15/0.42 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasapinj1 Bool) % 0.15/0.42 (declare-const tptp.ulamvar1 Bool) % 0.15/0.42 (declare-const tptp.induction2lem_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.15/0.42 (declare-const tptp.apnotvar Bool) % 0.15/0.42 (declare-const tptp.pushprop_lthm_orig Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.15/0.42 (declare-const tptp.hoaslaminj Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.15/0.42 (declare-const tptp.induction2lem_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3 Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem2 Bool) % 0.15/0.42 (declare-const tptp.termmset_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem1 Bool) % 0.15/0.42 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasapnotvar Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem0 Bool) % 0.15/0.42 (declare-const tptp.hoasinduction Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_gthm Bool) % 0.15/0.42 (declare-const tptp.axapp Bool) % 0.15/0.42 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.15/0.42 (declare-const tptp.ulamvarind Bool) % 0.15/0.42 (declare-const tptp.induction Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.15/0.42 (declare-const tptp.termmset_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.15/0.42 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.15/0.42 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem2v2 Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.15/0.42 (declare-const tptp.axclos Bool) % 0.15/0.42 (declare-const tptp.axassoc Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.15/0.42 (declare-const tptp.pushprop_lthm Bool) % 0.15/0.42 (declare-const tptp.apinj2 Bool) % 0.15/0.42 (declare-const tptp.apinj1 Bool) % 0.15/0.42 (declare-const tptp.hoasapinj2_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.15/0.42 (declare-const tptp.hoasapinj1_lthm Bool) % 0.15/0.42 (declare-const tptp.hoaslaminj_lthm Bool) % 0.15/0.42 (declare-const tptp.axvarcons Bool) % 0.15/0.42 (declare-const tptp.axscons Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.15/0.42 (declare-const tptp.d_one tptp.d_term) % 0.15/0.42 (declare-const tptp.hoaslamnotap Bool) % 0.15/0.42 (declare-const tptp.ulamvarsh Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem3v2 Bool) % 0.15/0.42 (declare-const tptp.axshiftcons Bool) % 0.15/0.42 (declare-const tptp.id tptp.subst) % 0.15/0.42 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 0.15/0.42 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.15/0.42 (declare-const tptp.one tptp.term) % 0.15/0.42 (declare-const tptp.substmonoid_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.15/0.42 (declare-const tptp.sh tptp.subst) % 0.15/0.42 (declare-const tptp.termmset Bool) % 0.15/0.42 (declare-const tptp.induction2 Bool) % 0.15/0.42 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 0.15/0.42 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.15/0.42 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.15/0.42 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.15/0.42 (declare-const tptp.axvarid Bool) % 0.15/0.42 (declare-const tptp.d_id tptp.d_subst) % 0.15/0.42 (declare-const tptp.var (-> tptp.term Bool)) % 0.15/0.42 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 0.15/0.42 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.15/0.42 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.15/0.42 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.15/0.42 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.15/0.42 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 0.15/0.42 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.15/0.42 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.15/0.42 (declare-const tptp.induction2_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3a Bool) % 0.15/0.42 (declare-const tptp.lamnotvar Bool) % 0.15/0.42 (declare-const tptp.substmonoid Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3b Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.15/0.42 (declare-const tptp.pushprop Bool) % 0.15/0.42 (declare-const tptp.substmonoid_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.15/0.42 (declare-const tptp.induction2_lthm Bool) % 0.15/0.42 (declare-const tptp.hoaslaminj_gthm Bool) % 0.15/0.42 (declare-const tptp.axidl Bool) % 0.15/0.42 (declare-const tptp.hoaslamnotvar Bool) % 0.15/0.42 (declare-const tptp.hoasapinj1_gthm Bool) % 0.15/0.42 (declare-const tptp.lamnotap Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasapinj2_gthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.15/0.42 (declare-const tptp.axabs Bool) % 0.15/0.42 (declare-const tptp.pushprop_gthm Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem0 Bool) % 0.15/0.42 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.15/0.42 (declare-const tptp.laminj Bool) % 0.15/0.42 (declare-const tptp.pushprop_lem1 Bool) % 0.15/0.42 (declare-const tptp.axidr Bool) % 0.15/0.42 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 0.15/0.42 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.15/0.42 (define @t3 () (_ @t2 tptp.id)) % 0.15/0.42 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.15/0.42 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 0.15/0.42 (define @t6 () (_ tptp.lam @t5)) % 0.15/0.42 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 0.15/0.42 (define @t8 () (@var "A" tptp.term)) % 0.15/0.42 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 0.15/0.42 (define @t10 () (not @t9)) % 0.15/0.42 (define @t11 () (@list @t8)) % 0.15/0.42 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 0.15/0.42 (define @t13 () (@var "N" tptp.subst)) % 0.15/0.42 (define @t14 () (_ tptp.sub @t8)) % 0.15/0.42 (define @t15 () (_ @t14 @t13)) % 0.15/0.42 (define @t16 () (@var "M" tptp.subst)) % 0.15/0.42 (define @t17 () (_ tptp.comp @t16)) % 0.15/0.42 (define @t18 () (_ @t17 @t13)) % 0.15/0.42 (define @t19 () (_ (_ @t4 @t16) @t8)) % 0.15/0.42 (define @t20 () (@list @t16 @t8 @t13)) % 0.15/0.42 (define @t21 () (not (forall @t20 (= (_ (_ tptp.sub @t19) @t13) (_ (_ @t4 @t18) @t15))))) % 0.15/0.42 (define @t22 () (@list @t4)) % 0.15/0.42 (define @t23 () (not (forall @t22 (or @t21 @t12 @t7)))) % 0.15/0.42 (define @t24 () (@var "B" tptp.term)) % 0.15/0.42 (define @t25 () (_ @t14 tptp.id)) % 0.15/0.42 (define @t26 () (_ tptp.ap @t25)) % 0.15/0.42 (define @t27 () (not (_ (_ @t3 @t24) tptp.id))) % 0.15/0.42 (define @t28 () (@list @t8 @t24)) % 0.15/0.42 (define @t29 () (not (forall @t28 (or @t10 @t27 (_ (_ @t3 (_ @t26 @t24)) tptp.id))))) % 0.15/0.42 (define @t30 () (@var "K" tptp.subst)) % 0.15/0.42 (define @t31 () (_ (_ (_ @t2 @t16) @t8) (_ (_ tptp.comp @t30) @t13))) % 0.15/0.42 (define @t32 () (_ (_ (_ @t2 (_ @t17 @t30)) (_ @t14 @t30)) @t13)) % 0.15/0.42 (define @t33 () (@list @t16 @t8 @t13 @t30)) % 0.15/0.42 (define @t34 () (not (forall @t33 (or (not @t32) @t31)))) % 0.15/0.42 (define @t35 () (not (forall @t33 (or (not @t31) @t32)))) % 0.15/0.42 (define @t36 () (forall (@list @t2 @t1) (or @t35 @t34 (not (forall @t11 (or (not (_ tptp.var @t25)) @t9))) @t29 @t23 (_ (_ @t3 @t1) tptp.id)))) % 0.15/0.42 (define @t37 () (@var "Bound_variable_2931" tptp.term)) % 0.15/0.42 (define @t38 () (@var "Q" (-> tptp.term Bool))) % 0.15/0.42 (define @t39 () (_ tptp.push @t24)) % 0.15/0.42 (define @t40 () (_ @t39 tptp.id)) % 0.15/0.42 (define @t41 () (not (_ @t38 @t24))) % 0.15/0.42 (define @t42 () (@list @t24)) % 0.15/0.42 (define @t43 () (@var "X" tptp.term)) % 0.15/0.42 (define @t44 () (_ (_ @t3 @t43) tptp.id)) % 0.15/0.42 (define @t45 () (_ @t38 @t43)) % 0.15/0.42 (define @t46 () (= @t45 @t44)) % 0.15/0.42 (define @t47 () (@list @t43)) % 0.15/0.42 (define @t48 () (forall @t47 @t46)) % 0.15/0.42 (define @t49 () (not @t48)) % 0.15/0.42 (define @t50 () (forall (@list @t2 @t38 @t37) (or @t23 @t49 (not (forall @t42 (or @t41 (_ @t38 (_ (_ tptp.sub @t37) @t40))))) (_ @t38 (_ tptp.lam @t37))))) % 0.15/0.42 (define @t51 () (forall @t11 (= @t8 @t25))) % 0.15/0.42 (define @t52 () (@var "Bound_variable_2367" tptp.term)) % 0.15/0.42 (define @t53 () (@var "P" (-> tptp.term Bool))) % 0.15/0.42 (define @t54 () (_ tptp.lam @t8)) % 0.15/0.42 (define @t55 () (_ @t53 @t54)) % 0.15/0.42 (define @t56 () (not (_ @t53 @t24))) % 0.15/0.42 (define @t57 () (not (forall @t11 (or (not (forall @t42 (or @t56 (_ @t53 (_ @t14 @t40))))) @t55)))) % 0.15/0.42 (define @t58 () (_ tptp.ap @t8)) % 0.15/0.42 (define @t59 () (_ @t53 @t8)) % 0.15/0.42 (define @t60 () (not @t59)) % 0.15/0.42 (define @t61 () (not (forall @t28 (or @t60 @t56 (_ @t53 (_ @t58 @t24)))))) % 0.15/0.42 (define @t62 () (not (forall @t11 (or (not (_ tptp.var @t8)) @t59)))) % 0.15/0.42 (define @t63 () (forall (@list @t53 @t52) (or @t62 @t61 @t57 (_ @t53 @t52)))) % 0.15/0.42 (define @t64 () (@list @t38)) % 0.15/0.42 (define @t65 () (forall @t64 @t49)) % 0.15/0.42 (define @t66 () (not @t65)) % 0.15/0.42 (define @t67 () (@list @t2)) % 0.15/0.42 (define @t68 () (forall @t67 @t66)) % 0.15/0.42 (define @t69 () (@var "Bound_variable_2910" tptp.term)) % 0.15/0.42 (define @t70 () (forall (@list @t2 @t38 @t69) (or @t35 @t34 @t23 @t49 (not (forall @t42 (or @t41 (_ @t38 (_ (_ tptp.sub @t69) @t40))))) (_ @t38 (_ tptp.lam @t69))))) % 0.15/0.42 (define @t71 () (_ (_ tptp.push @t8) @t16)) % 0.15/0.42 (define @t72 () (forall @t47 (= @t45 (_ @t53 (_ (_ tptp.sub @t43) @t71))))) % 0.15/0.42 (define @t73 () (not @t72)) % 0.15/0.42 (define @t74 () (forall (@list @t53 @t8 @t16) (not (forall @t64 @t73)))) % 0.15/0.42 (define @t75 () (_ tptp.comp tptp.sh)) % 0.15/0.42 (define @t76 () (@list @t8 @t16)) % 0.15/0.42 (define @t77 () (forall @t76 (= @t16 (_ @t75 @t71)))) % 0.15/0.42 (define @t78 () (@var "K" (-> tptp.term Bool))) % 0.15/0.42 (define @t79 () (forall (@list @t53 @t78 @t8 @t16 @t24) (or @t60 (_ @t78 (_ @t14 (_ @t39 @t16)))))) % 0.15/0.42 (define @t80 () (_ tptp.sub tptp.one)) % 0.15/0.42 (define @t81 () (forall @t76 (= @t8 (_ @t80 @t71)))) % 0.15/0.42 (define @t82 () (@var "Bound_variable_2605" tptp.term)) % 0.15/0.42 (define @t83 () (@var "Bound_variable_2603" tptp.term)) % 0.15/0.42 (define @t84 () (_ tptp.d2subst tptp.d_id)) % 0.15/0.42 (define @t85 () (_ tptp.d2term tptp.d_one)) % 0.15/0.42 (define @t86 () (@var "Bound_variable_3295" tptp.term)) % 0.15/0.42 (define @t87 () (forall (@list @t2 @t86) (or @t29 @t23 (_ (_ @t3 @t86) tptp.id)))) % 0.15/0.42 (define @t88 () (@var "Bound_variable_3232" tptp.term)) % 0.15/0.42 (define @t89 () (forall (@list @t2 @t88) (or @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t88) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t88)) tptp.id)))) % 0.15/0.42 (define @t90 () (@list @t16)) % 0.15/0.42 (define @t91 () (forall @t90 (= @t16 (_ @t17 tptp.id)))) % 0.15/0.42 (define @t92 () (forall @t90 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 0.15/0.42 (define @t93 () (and @t92 @t91)) % 0.15/0.42 (define @t94 () (_ (_ tptp.push tptp.one) tptp.sh)) % 0.15/0.42 (define @t95 () (_ tptp.sub @t24)) % 0.15/0.42 (define @t96 () (forall @t42 (not (forall @t22 (not (= @t5 (_ @t95 @t94))))))) % 0.15/0.42 (define @t97 () (@var "Bound_variable_2342" tptp.subst)) % 0.15/0.42 (define @t98 () (@var "Bound_variable_2340" tptp.term)) % 0.15/0.42 (define @t99 () (forall (@list @t53 @t98 @t97) (or @t61 @t57 (not (forall @t42 (or (not (_ tptp.var @t24)) (_ @t53 (_ @t95 @t97))))) (_ @t53 (_ (_ tptp.sub @t98) @t97))))) % 0.15/0.42 (define @t100 () (forall @t42 (not (forall @t22 (not (forall @t76 (= (_ @t95 @t71) @t19))))))) % 0.15/0.42 (define @t101 () (@var "Bound_variable_3211" tptp.term)) % 0.15/0.42 (define @t102 () (forall (@list @t2 @t101) (or @t35 @t34 @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t101) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t101)) tptp.id)))) % 0.15/0.42 (define @t103 () (@var "Bound_variable_3046" tptp.term)) % 0.15/0.42 (define @t104 () (_ tptp.sub @t103)) % 0.15/0.42 (define @t105 () (forall (@list @t2 @t103) (or @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ @t104 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t104 @t94))) tptp.id)))) % 0.15/0.42 (define @t106 () (= @t8 @t24)) % 0.15/0.42 (define @t107 () (forall @t28 (or (not (= @t54 (_ tptp.lam @t24))) @t106))) % 0.15/0.42 (define @t108 () (@var "Bound_variable_2551" tptp.term)) % 0.15/0.42 (define @t109 () (@var "Bound_variable_2549" tptp.subst)) % 0.15/0.42 (define @t110 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 0.15/0.42 (define @t111 () (forall (@list @t4 @t110 @t109 @t108) (or @t21 (not (forall @t20 (= (_ (_ tptp.sub (_ (_ @t110 @t16) @t8)) @t13) (_ (_ @t110 @t18) @t15)))) (not (= @t6 (_ tptp.lam (_ (_ @t110 tptp.sh) tptp.one)))) (= (_ (_ @t4 @t109) @t108) (_ (_ @t110 @t109) @t108))))) % 0.15/0.42 (define @t112 () (@var "D" tptp.term)) % 0.15/0.42 (define @t113 () (@var "C" tptp.term)) % 0.15/0.42 (define @t114 () (not (= (_ @t26 @t113) (_ (_ tptp.ap (_ @t95 tptp.id)) @t112)))) % 0.15/0.42 (define @t115 () (@list @t8 @t24 @t113 @t112)) % 0.15/0.42 (define @t116 () (forall @t115 (or @t114 @t106))) % 0.15/0.42 (define @t117 () (not (= (_ @t58 @t113) (_ (_ tptp.ap @t24) @t112)))) % 0.15/0.42 (define @t118 () (forall @t115 (or @t117 @t106))) % 0.15/0.42 (define @t119 () (= @t113 @t112)) % 0.15/0.42 (define @t120 () (forall @t115 (or @t114 @t119))) % 0.15/0.42 (define @t121 () (forall @t115 (or @t117 @t119))) % 0.15/0.42 (define @t122 () (@var "Bound_variable_2822" tptp.term)) % 0.15/0.42 (define @t123 () (@var "Bound_variable_2820" tptp.term)) % 0.15/0.42 (define @t124 () (@var "Bound_variable_2140" tptp.term)) % 0.15/0.42 (define @t125 () (forall (@list @t53 @t124) (or @t62 @t61 (not (forall @t11 (or @t60 @t55))) (_ @t53 @t124)))) % 0.15/0.42 (define @t126 () (= tptp.hoasinduction_lem0 @t68)) % 0.15/0.42 (define @t127 () (forall (@list @t53 @t38 @t8 @t16) (or @t60 @t73 (_ @t38 tptp.one)))) % 0.15/0.42 (define @t128 () (@var "Bound_variable_3001" tptp.term)) % 0.15/0.42 (define @t129 () (@var "Bound_variable_2999" tptp.term)) % 0.15/0.42 (define @t130 () (forall (@list @t2 @t129 @t128) (or @t35 @t34 @t29 (not (_ (_ @t3 @t129) tptp.id)) (not (_ (_ @t3 @t128) tptp.id)) (_ (_ @t3 (_ (_ tptp.ap @t129) @t128)) tptp.id)))) % 0.15/0.42 (define @t131 () (@var "Bound_variable_3171" tptp.term)) % 0.15/0.42 (define @t132 () (_ tptp.sub @t131)) % 0.15/0.42 (define @t133 () (@var "Bound_variable_3094" tptp.subst)) % 0.15/0.42 (define @t134 () (@var "Bound_variable_3090" tptp.subst)) % 0.15/0.42 (define @t135 () (_ (_ tptp.comp @t134) @t133)) % 0.15/0.42 (define @t136 () (@var "Bound_variable_3092" tptp.term)) % 0.15/0.42 (define @t137 () (_ (_ tptp.sub @t136) @t133)) % 0.15/0.42 (define @t138 () (@var "Bound_variable_3149" tptp.term)) % 0.15/0.42 (define @t139 () (_ tptp.sub @t138)) % 0.15/0.42 (define @t140 () (@var "Bound_variable_3076" tptp.subst)) % 0.15/0.42 (define @t141 () (@var "Bound_variable_3072" tptp.subst)) % 0.15/0.42 (define @t142 () (@var "Bound_variable_3074" tptp.term)) % 0.15/0.42 (define @t143 () (@list @t2 @t38)) % 0.15/0.42 (define @t144 () (lambda @t143 @t48)) % 0.15/0.42 (define @t145 () (= tptp.hoasinduction_p_and_p_prime @t144)) % 0.15/0.42 (define @t146 () (@var "DS2" tptp.d_subst)) % 0.15/0.42 (define @t147 () (@var "DS1" tptp.d_subst)) % 0.15/0.42 (define @t148 () (@var "DS" tptp.d_subst)) % 0.15/0.42 (define @t149 () (@list @t148)) % 0.15/0.42 (define @t150 () (@var "S" tptp.subst)) % 0.15/0.42 (define @t151 () (@var "DT2" tptp.d_term)) % 0.15/0.42 (define @t152 () (@var "DT1" tptp.d_term)) % 0.15/0.42 (define @t153 () (@var "DT" tptp.d_term)) % 0.15/0.42 (define @t154 () (@list @t153)) % 0.15/0.42 (define @t155 () (@var "T" tptp.term)) % 0.15/0.42 (define @t156 () (_ (_ tptp.hoasinduction_p_and_p_prime @t2) @t38)) % 0.15/0.42 (define @t157 () (exists @t64 @t156)) % 0.15/0.42 (define @t158 () (forall @t67 @t157)) % 0.15/0.42 (define @t159 () (= tptp.hoasinduction_lem0 @t158)) % 0.15/0.42 (define @t160 () (not @t159)) % 0.15/0.42 (define @t161 () (tptp.d2subst tptp.d_id)) % 0.15/0.42 (define @t162 () (_ @t38 @t43)) % 0.15/0.42 (define @t163 () (forall @t47 (= @t162 (_ @t2 @t161 @t43 @t161)))) % 0.15/0.42 (define @t164 () (forall @t67 (not (forall @t64 (not @t163))))) % 0.15/0.42 (define @t165 () (_ (lambda @t143 @t163) @t2 @t38)) % 0.15/0.42 (define @t166 () (not @t165)) % 0.15/0.42 (define @t167 () (forall @t64 @t166)) % 0.15/0.42 (define @t168 () (not @t167)) % 0.15/0.42 (define @t169 () (forall @t67 @t168)) % 0.15/0.42 (define @t170 () (= @t164 @t169)) % 0.15/0.42 (define @t171 () (_ @t2 @t84 @t43 @t84)) % 0.15/0.42 (define @t172 () (= @t162 @t171)) % 0.15/0.42 (define @t173 () (forall @t47 @t172)) % 0.15/0.42 (define @t174 () (lambda @t143 @t173)) % 0.15/0.42 (define @t175 () (_ @t2 tptp.id @t43 tptp.id)) % 0.15/0.42 (define @t176 () (= @t162 @t175)) % 0.15/0.42 (define @t177 () (forall @t47 @t176)) % 0.15/0.42 (define @t178 () (lambda @t143 @t177)) % 0.15/0.42 (define @t179 () (tptp.hoasinduction_p_and_p_prime @t2 @t38)) % 0.15/0.42 (define @t180 () (not @t179)) % 0.15/0.42 (define @t181 () (forall @t64 @t180)) % 0.15/0.42 (define @t182 () (not @t181)) % 0.15/0.42 (define @t183 () (forall @t67 @t182)) % 0.15/0.42 (define @t184 () (not @t173)) % 0.15/0.42 (define @t185 () (forall @t64 @t184)) % 0.15/0.42 (define @t186 () (not @t185)) % 0.15/0.42 (define @t187 () (forall @t67 @t186)) % 0.15/0.42 (define @t188 () (not @t177)) % 0.15/0.42 (define @t189 () (forall @t64 @t188)) % 0.15/0.42 (define @t190 () (not @t189)) % 0.15/0.42 (define @t191 () (forall @t67 @t190)) % 0.15/0.42 (define @t192 () (= tptp.hoasinduction_lem0 @t183)) % 0.15/0.42 (define @t193 () (not @t156)) % 0.15/0.42 (define @t194 () (forall @t64 @t193)) % 0.15/0.42 (define @t195 () (not @t194)) % 0.15/0.42 (assume @p1 (and (forall (@list @t155) (exists @t154 (= @t155 (_ tptp.d2term @t153)))) (forall @t154 (= @t153 tptp.d_one)) (forall (@list @t152 @t151) (=> (= (_ tptp.d2term @t152) (_ tptp.d2term @t151)) (= @t152 @t151))) (forall (@list @t150) (exists @t149 (= @t150 (_ tptp.d2subst @t148)))) (forall @t149 (= @t148 tptp.d_id)) (forall (@list @t147 @t146) (=> (= (_ tptp.d2subst @t147) (_ tptp.d2subst @t146)) (= @t147 @t146))) (= tptp.one @t85) (= (_ (_ tptp.ap @t85) @t85) @t85) (= (_ tptp.lam @t85) @t85) (= (_ (_ tptp.sub @t85) @t84) @t85) (= tptp.id @t84) (= tptp.sh @t84) (= (_ (_ tptp.push @t85) @t84) @t84) (= (_ (_ tptp.comp @t84) @t84) @t84) (= (_ (_ (_ (_ tptp.hoasap @t84) @t85) @t84) @t85) @t85) (= tptp.hoaslam (lambda (@list (@var "Bound_variable_4913" tptp.subst) (@var "Bound_variable_4915" (-> tptp.subst tptp.term tptp.term))) @t85)) @t145 (= tptp.pushprop_p_and_p_prime (lambda (@list @t8 @t16 @t53 @t38) @t72)) (not (_ tptp.var @t85)) (= tptp.pushprop_lem1v2 @t127) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t28 (or (not (= (_ @t14 tptp.sh) (_ @t95 tptp.sh))) @t106))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t99) (= tptp.hoasinduction_lem3v2_f @t100) tptp.axvarshift (= tptp.hoasapinj2 @t120) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t116) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t81 (=> @t77 (=> @t91 (=> @t125 @t99))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t100) (= tptp.hoasinduction_lthm (=> @t63 (=> @t130 (=> @t102 @t36)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t68 (=> @t63 (=> @t51 (=> @t50 @t87))))) (= tptp.hoaslaminj @t111) (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t131) (or (not (forall (@list @t4 @t138) (or @t12 @t7 (not (forall (@list @t141 @t142 @t140) (= (_ (_ tptp.sub (_ (_ @t4 @t141) @t142)) @t140) (_ (_ tptp.sub (_ @t139 (_ (_ tptp.push @t142) @t141))) @t140)))) (not (forall (@list @t134 @t136 @t133) (= (_ (_ @t4 @t135) @t137) (_ @t139 (_ (_ tptp.push @t137) @t135)))))))) (not (forall @t42 (or @t27 (_ (_ @t3 (_ @t132 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t132 @t94))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t105) (= tptp.hoasinduction_lem3 @t102) (= tptp.hoasinduction_lem2 @t130) (= tptp.termmset_lthm (=> @t51 @t51)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t81 @t127)) tptp.hoasapnotvar @t126 (= tptp.hoasinduction @t36) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t96) tptp.ulamvarind (= tptp.induction @t125) (= tptp.hoasinduction_lem3a_lthm (=> @t51 (=> @t105 @t89))) tptp.termmset_gthm (= tptp.hoasinduction_lem3aa @t105) 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 @t38 @t123 @t122) (or @t35 @t34 @t29 @t49 (not (_ @t38 @t123)) (not (_ @t38 @t122)) (_ @t38 (_ (_ tptp.ap @t123) @t122))))) tptp.pushprop_lthm (= tptp.apinj2 @t121) (= tptp.apinj1 @t118) (= tptp.hoasapinj2_lthm (=> @t121 @t120)) (= tptp.hoasinduction_lem3v2a @t50) (= tptp.hoasapinj1_lthm (=> @t51 (=> @t118 @t116))) (= tptp.hoaslaminj_lthm (=> @t81 (=> @t77 (=> @t107 @t111)))) (= tptp.axvarcons @t81) (= tptp.axscons (forall @t90 (= @t16 (_ (_ tptp.push (_ @t80 @t16)) (_ @t75 @t16))))) tptp.hoasinduction_lem2v2_gthm (= tptp.axidr @t91) (= tptp.pushprop_lem1 @t79) (= tptp.laminj @t107) (= tptp.hoasinduction_lem3_lthm (=> @t51 (=> @t105 @t102))) (= tptp.pushprop_lem0 @t74) tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t100 (=> @t51 @t50))) tptp.hoasinduction_lem2_lthm tptp.hoasapinj2_gthm tptp.hoasinduction_lem1_lthm (not tptp.lamnotap) tptp.hoasapinj1_gthm tptp.hoaslamnotvar (= tptp.axidl @t92) tptp.hoaslaminj_gthm (= tptp.induction2_lthm (=> @t51 (=> @t99 @t63))) (= tptp.hoasinduction_lem0_lthm @t68) (= tptp.substmonoid_lthm (=> @t92 (=> @t91 @t93))) tptp.pushprop tptp.hoasinduction_lem3_gthm tptp.hoasinduction_lem2_gthm (= tptp.hoasinduction_lem3b @t96) (= tptp.substmonoid @t93) tptp.lamnotvar (= tptp.hoasinduction_lem3a @t89) tptp.hoasinduction_lem1_gthm (= tptp.hoasinduction_no_psi_cond @t87) tptp.induction2_gthm tptp.pushprop_lem2v2_lthm (not (_ (_ (_ tptp.hoasvar @t84) @t85) @t84)) (= tptp.hoaslamnotap (forall (@list @t4 @t83 @t82) (or @t21 (not (= @t6 (_ (_ tptp.ap (_ (_ tptp.sub @t83) tptp.id)) @t82)))))) tptp.substmonoid_gthm tptp.ulamvarsh (= tptp.induction2 @t63) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t81 (=> @t77 @t79))) (= tptp.hoasinduction_lem3v2 @t70) (= tptp.axshiftcons @t77) (= tptp.termmset @t51) (= tptp.pushprop_lem0_lthm @t74) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t51 @t70)) (= tptp.axvarid @t51) (= tptp.hoasinduction_lthm_3 (=> @t68 (=> @t63 (=> @t51 (=> @t50 @t36))))))) % 0.15/0.42 (assume @p2 @t160) % 0.15/0.42 (assume @p3 true) % 0.15/0.42 (step @p4 :rule evaluate :args ((not true))) % 0.15/0.42 (step @p5 :rule eq-refl :args (@t164)) % 0.15/0.42 (step @p6 :rule beta-reduce :args ((= @t165 @t163))) % 0.15/0.42 (step @p7 :rule cong :premises (@p6) :args (@t166)) % 0.15/0.42 (step @p8 :rule cong :premises (@p7) :args (@t167)) % 0.15/0.42 (step @p9 :rule cong :premises (@p8) :args (@t168)) % 0.15/0.42 (step @p10 :rule cong :premises (@p9) :args (@t169)) % 0.15/0.42 (step @p11 :rule refl :args (@t164)) % 0.15/0.42 (step @p12 :rule cong :premises (@p11 @p10) :args (@t170)) % 0.15/0.42 (step @p13 :rule trans :premises (@p12 @p5)) % 0.15/0.42 (step @p14 :rule cong :premises (@p13) :args ((not @t170))) % 0.15/0.42 (step @p15 :rule trans :premises (@p14 @p4)) % 0.15/0.42 (step @p16 :rule refl :args (@t38)) % 0.15/0.42 (step @p17 :rule refl :args (@t2)) % 0.15/0.42 (step @p18 :rule refl :args (@t161)) % 0.15/0.42 (step @p19 :rule refl :args (@t84)) % 0.15/0.42 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t84 @t161))) % 0.15/0.42 (step @p21 :rule symm :premises (@p20)) % 0.15/0.42 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.15/0.42 (step @p23 :rule refl :args (@t43)) % 0.15/0.42 (step @p24 :rule cong :premises (@p22 @p23 @p22) :args (@t171)) % 0.15/0.42 (step @p25 :rule refl :args (@t162)) % 0.15/0.42 (step @p26 :rule cong :premises (@p25 @p24) :args (@t172)) % 0.15/0.42 (step @p27 :rule cong :premises (@p26) :args (@t173)) % 0.15/0.42 (step @p28 :rule cong :premises (@p27) :args (@t174)) % 0.15/0.42 (step @p29 :rule refl :args (tptp.hoasinduction_p_and_p_prime)) % 0.15/0.42 (step @p30 :rule cong :premises (@p29 @p28) :args ((= tptp.hoasinduction_p_and_p_prime @t174))) % 0.15/0.42 (step @p31 :rule and_elim :premises (@p1) :args (10)) % 0.15/0.42 (step @p32 :rule refl :args (@t43)) % 0.15/0.42 (step @p33 :rule cong :premises (@p31 @p32 @p31) :args (@t175)) % 0.15/0.42 (step @p34 :rule refl :args (@t162)) % 0.15/0.42 (step @p35 :rule cong :premises (@p34 @p33) :args (@t176)) % 0.15/0.42 (step @p36 :rule cong :premises (@p35) :args (@t177)) % 0.15/0.42 (step @p37 :rule cong :premises (@p36) :args (@t178)) % 0.15/0.42 (step @p38 :rule cong :premises (@p29 @p37) :args ((= tptp.hoasinduction_p_and_p_prime @t178))) % 0.15/0.42 (step @p39 :rule trans :premises (@p38 @p30)) % 0.15/0.42 (step @p40 :rule refl :args (@t175)) % 0.15/0.42 (step @p41 :rule refl :args (@t44)) % 0.15/0.42 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t44 @t175))) % 0.15/0.42 (step @p43 :rule symm :premises (@p42)) % 0.15/0.42 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.15/0.42 (step @p45 :rule refl :args (@t162)) % 0.15/0.42 (step @p46 :rule refl :args (@t45)) % 0.15/0.42 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t45 @t162))) % 0.15/0.42 (step @p48 :rule symm :premises (@p47)) % 0.15/0.42 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.15/0.42 (step @p50 :rule cong :premises (@p49 @p44) :args (@t46)) % 0.15/0.42 (step @p51 :rule cong :premises (@p50) :args (@t48)) % 0.15/0.42 (step @p52 :rule cong :premises (@p51) :args (@t144)) % 0.15/0.42 (step @p53 :rule cong :premises (@p29 @p52) :args (@t145)) % 0.15/0.42 (step @p54 :rule and_elim :premises (@p1) :args (16)) % 0.15/0.42 (step @p55 :rule eq_resolve :premises (@p54 @p53)) % 0.15/0.42 (step @p56 :rule eq_resolve :premises (@p55 @p39)) % 0.15/0.42 (step @p57 :rule ho_cong :premises (@p56 @p17 @p16)) % 0.15/0.42 (step @p58 :rule cong :premises (@p57) :args (@t180)) % 0.15/0.42 (step @p59 :rule cong :premises (@p58) :args (@t181)) % 0.15/0.42 (step @p60 :rule cong :premises (@p59) :args (@t182)) % 0.15/0.42 (step @p61 :rule cong :premises (@p60) :args (@t183)) % 0.15/0.42 (step @p62 :rule cong :premises (@p27) :args (@t184)) % 0.15/0.42 (step @p63 :rule cong :premises (@p62) :args (@t185)) % 0.15/0.42 (step @p64 :rule cong :premises (@p63) :args (@t186)) % 0.15/0.42 (step @p65 :rule cong :premises (@p64) :args (@t187)) % 0.15/0.42 (step @p66 :rule refl :args (tptp.hoasinduction_lem0)) % 0.15/0.42 (step @p67 :rule cong :premises (@p66 @p65) :args ((= tptp.hoasinduction_lem0 @t187))) % 0.15/0.42 (step @p68 :rule cong :premises (@p36) :args (@t188)) % 0.15/0.42 (step @p69 :rule cong :premises (@p68) :args (@t189)) % 0.15/0.42 (step @p70 :rule cong :premises (@p69) :args (@t190)) % 0.15/0.42 (step @p71 :rule cong :premises (@p70) :args (@t191)) % 0.15/0.42 (step @p72 :rule cong :premises (@p66 @p71) :args ((= tptp.hoasinduction_lem0 @t191))) % 0.15/0.42 (step @p73 :rule trans :premises (@p72 @p67)) % 0.15/0.42 (step @p74 :rule cong :premises (@p51) :args (@t49)) % 0.15/0.42 (step @p75 :rule cong :premises (@p74) :args (@t65)) % 0.15/0.42 (step @p76 :rule cong :premises (@p75) :args (@t66)) % 0.15/0.42 (step @p77 :rule cong :premises (@p76) :args (@t68)) % 0.15/0.42 (step @p78 :rule cong :premises (@p66 @p77) :args (@t126)) % 0.15/0.42 (step @p79 :rule and_elim :premises (@p1) :args (51)) % 0.15/0.42 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.15/0.42 (step @p81 :rule eq_resolve :premises (@p80 @p73)) % 0.15/0.42 (step @p82 :rule cong :premises (@p81 @p61) :args (@t192)) % 0.15/0.42 (step @p83 :rule cong :premises (@p82) :args ((not @t192))) % 0.15/0.42 (step @p84 :rule trans :premises (@p83 @p15)) % 0.15/0.42 (step @p85 :rule refl :args (@t179)) % 0.15/0.42 (step @p86 :rule refl :args (@t156)) % 0.15/0.42 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t156 @t179))) % 0.15/0.42 (step @p88 :rule symm :premises (@p87)) % 0.15/0.42 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.15/0.42 (step @p90 :rule cong :premises (@p89) :args (@t193)) % 0.15/0.42 (step @p91 :rule cong :premises (@p90) :args (@t194)) % 0.15/0.42 (step @p92 :rule cong :premises (@p91) :args (@t195)) % 0.15/0.42 (step @p93 :rule exists-elim :args ((= @t157 @t195))) % 0.15/0.42 (step @p94 :rule trans :premises (@p93 @p92)) % 0.15/0.42 (step @p95 :rule cong :premises (@p94) :args (@t158)) % 0.15/0.42 (step @p96 :rule cong :premises (@p66 @p95) :args (@t159)) % 0.15/0.42 (step @p97 :rule cong :premises (@p96) :args (@t160)) % 0.15/0.42 (step @p98 :rule eq_resolve :premises (@p2 @p97)) % 0.15/0.42 (step @p99 false :rule eq_resolve :premises (@p98 @p84)) % 0.15/0.42 ) % 0.15/0.42 % SZS output end Proof % 0.15/0.43 % cvc5 exiting %------------------------------------------------------------------------------