%------------------------------------------------------------------------------ % 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 : n014.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 09:07:14 AM UTC 2026 % Result : Theorem 0.40s 0.65s % Output : Proof 0.40s % 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. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n014.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 23:02:13 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.55 %----Proving TH0 % 0.40/0.65 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.65 % SZS status Theorem % 0.40/0.65 % SZS output start Proof % 0.40/0.65 ( % 0.40/0.65 (declare-sort tptp.term 0) % 0.40/0.65 (declare-sort tptp.subst 0) % 0.40/0.65 (declare-sort tptp.d_term 0) % 0.40/0.65 (declare-sort tptp.d_subst 0) % 0.40/0.65 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 0.40/0.65 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 0.40/0.65 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 0.40/0.65 (declare-const tptp.pushprop_lem1v2 Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.40/0.65 (declare-const tptp.axmap Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.40/0.65 (declare-const tptp.shinj Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.40/0.65 (declare-const tptp.induction2lem Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.40/0.65 (declare-const tptp.axvarshift Bool) % 0.40/0.65 (declare-const tptp.hoasapinj2 Bool) % 0.40/0.65 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasapinj1 Bool) % 0.40/0.65 (declare-const tptp.ulamvar1 Bool) % 0.40/0.65 (declare-const tptp.induction2lem_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.40/0.65 (declare-const tptp.apnotvar Bool) % 0.40/0.65 (declare-const tptp.pushprop_lthm_orig Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.40/0.65 (declare-const tptp.hoaslaminj Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.40/0.65 (declare-const tptp.induction2lem_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3 Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem2 Bool) % 0.40/0.65 (declare-const tptp.termmset_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem1 Bool) % 0.40/0.65 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasapnotvar Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem0 Bool) % 0.40/0.65 (declare-const tptp.hoasinduction Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_gthm Bool) % 0.40/0.65 (declare-const tptp.axapp Bool) % 0.40/0.65 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.40/0.65 (declare-const tptp.ulamvarind Bool) % 0.40/0.65 (declare-const tptp.induction Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.40/0.65 (declare-const tptp.termmset_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.40/0.65 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.40/0.65 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem2v2 Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.40/0.65 (declare-const tptp.axclos Bool) % 0.40/0.65 (declare-const tptp.axassoc Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.40/0.65 (declare-const tptp.pushprop_lthm Bool) % 0.40/0.65 (declare-const tptp.apinj2 Bool) % 0.40/0.65 (declare-const tptp.apinj1 Bool) % 0.40/0.65 (declare-const tptp.hoasapinj2_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.40/0.65 (declare-const tptp.hoasapinj1_lthm Bool) % 0.40/0.65 (declare-const tptp.hoaslaminj_lthm Bool) % 0.40/0.65 (declare-const tptp.axvarcons Bool) % 0.40/0.65 (declare-const tptp.axscons Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.40/0.65 (declare-const tptp.d_one tptp.d_term) % 0.40/0.65 (declare-const tptp.hoaslamnotap Bool) % 0.40/0.65 (declare-const tptp.ulamvarsh Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem3v2 Bool) % 0.40/0.65 (declare-const tptp.axshiftcons Bool) % 0.40/0.65 (declare-const tptp.id tptp.subst) % 0.40/0.65 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 0.40/0.65 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.40/0.65 (declare-const tptp.one tptp.term) % 0.40/0.65 (declare-const tptp.substmonoid_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.40/0.65 (declare-const tptp.sh tptp.subst) % 0.40/0.65 (declare-const tptp.termmset Bool) % 0.40/0.65 (declare-const tptp.induction2 Bool) % 0.40/0.65 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 0.40/0.65 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.40/0.65 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.40/0.65 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.40/0.65 (declare-const tptp.axvarid Bool) % 0.40/0.65 (declare-const tptp.d_id tptp.d_subst) % 0.40/0.65 (declare-const tptp.var (-> tptp.term Bool)) % 0.40/0.65 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 0.40/0.65 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.40/0.65 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.40/0.65 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.40/0.65 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.40/0.65 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 0.40/0.65 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.40/0.65 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.40/0.65 (declare-const tptp.induction2_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3a Bool) % 0.40/0.65 (declare-const tptp.lamnotvar Bool) % 0.40/0.65 (declare-const tptp.substmonoid Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3b Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.40/0.65 (declare-const tptp.pushprop Bool) % 0.40/0.65 (declare-const tptp.substmonoid_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.40/0.65 (declare-const tptp.induction2_lthm Bool) % 0.40/0.65 (declare-const tptp.hoaslaminj_gthm Bool) % 0.40/0.65 (declare-const tptp.axidl Bool) % 0.40/0.65 (declare-const tptp.hoaslamnotvar Bool) % 0.40/0.65 (declare-const tptp.hoasapinj1_gthm Bool) % 0.40/0.65 (declare-const tptp.lamnotap Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasapinj2_gthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.40/0.65 (declare-const tptp.axabs Bool) % 0.40/0.65 (declare-const tptp.pushprop_gthm Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem0 Bool) % 0.40/0.65 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.40/0.65 (declare-const tptp.laminj Bool) % 0.40/0.65 (declare-const tptp.pushprop_lem1 Bool) % 0.40/0.65 (declare-const tptp.axidr Bool) % 0.40/0.65 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 0.40/0.65 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.40/0.65 (define @t3 () (_ @t2 tptp.id)) % 0.40/0.65 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.40/0.65 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 0.40/0.65 (define @t6 () (_ tptp.lam @t5)) % 0.40/0.65 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 0.40/0.65 (define @t8 () (@var "A" tptp.term)) % 0.40/0.65 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 0.40/0.65 (define @t10 () (not @t9)) % 0.40/0.65 (define @t11 () (@list @t8)) % 0.40/0.65 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 0.40/0.65 (define @t13 () (@var "N" tptp.subst)) % 0.40/0.65 (define @t14 () (_ tptp.sub @t8)) % 0.40/0.65 (define @t15 () (_ @t14 @t13)) % 0.40/0.65 (define @t16 () (@var "M" tptp.subst)) % 0.40/0.65 (define @t17 () (_ tptp.comp @t16)) % 0.40/0.65 (define @t18 () (_ @t17 @t13)) % 0.40/0.65 (define @t19 () (_ (_ @t4 @t16) @t8)) % 0.40/0.65 (define @t20 () (@list @t16 @t8 @t13)) % 0.40/0.65 (define @t21 () (not (forall @t20 (= (_ (_ tptp.sub @t19) @t13) (_ (_ @t4 @t18) @t15))))) % 0.40/0.65 (define @t22 () (@list @t4)) % 0.40/0.65 (define @t23 () (not (forall @t22 (or @t21 @t12 @t7)))) % 0.40/0.65 (define @t24 () (@var "B" tptp.term)) % 0.40/0.65 (define @t25 () (_ @t14 tptp.id)) % 0.40/0.65 (define @t26 () (_ tptp.ap @t25)) % 0.40/0.65 (define @t27 () (not (_ (_ @t3 @t24) tptp.id))) % 0.40/0.65 (define @t28 () (@list @t8 @t24)) % 0.40/0.65 (define @t29 () (not (forall @t28 (or @t10 @t27 (_ (_ @t3 (_ @t26 @t24)) tptp.id))))) % 0.40/0.65 (define @t30 () (@var "K" tptp.subst)) % 0.40/0.65 (define @t31 () (_ (_ (_ @t2 @t16) @t8) (_ (_ tptp.comp @t30) @t13))) % 0.40/0.65 (define @t32 () (_ (_ (_ @t2 (_ @t17 @t30)) (_ @t14 @t30)) @t13)) % 0.40/0.65 (define @t33 () (@list @t16 @t8 @t13 @t30)) % 0.40/0.65 (define @t34 () (not (forall @t33 (or (not @t32) @t31)))) % 0.40/0.65 (define @t35 () (not (forall @t33 (or (not @t31) @t32)))) % 0.40/0.65 (define @t36 () (forall (@list @t2 @t1) (or @t35 @t34 (not (forall @t11 (or (not (_ tptp.var @t25)) @t9))) @t29 @t23 (_ (_ @t3 @t1) tptp.id)))) % 0.40/0.65 (define @t37 () (@var "Bound_variable_2931" tptp.term)) % 0.40/0.65 (define @t38 () (@var "Q" (-> tptp.term Bool))) % 0.40/0.65 (define @t39 () (_ tptp.push @t24)) % 0.40/0.65 (define @t40 () (_ @t39 tptp.id)) % 0.40/0.65 (define @t41 () (not (_ @t38 @t24))) % 0.40/0.65 (define @t42 () (@list @t24)) % 0.40/0.65 (define @t43 () (@var "X" tptp.term)) % 0.40/0.65 (define @t44 () (_ @t38 @t43)) % 0.40/0.65 (define @t45 () (@list @t43)) % 0.40/0.65 (define @t46 () (forall @t45 (= @t44 (_ (_ @t3 @t43) tptp.id)))) % 0.40/0.65 (define @t47 () (not @t46)) % 0.40/0.65 (define @t48 () (forall (@list @t2 @t38 @t37) (or @t23 @t47 (not (forall @t42 (or @t41 (_ @t38 (_ (_ tptp.sub @t37) @t40))))) (_ @t38 (_ tptp.lam @t37))))) % 0.40/0.65 (define @t49 () (forall @t11 (= @t8 @t25))) % 0.40/0.65 (define @t50 () (@var "Bound_variable_2367" tptp.term)) % 0.40/0.65 (define @t51 () (@var "P" (-> tptp.term Bool))) % 0.40/0.65 (define @t52 () (_ tptp.lam @t8)) % 0.40/0.65 (define @t53 () (_ @t51 @t52)) % 0.40/0.65 (define @t54 () (not (_ @t51 @t24))) % 0.40/0.65 (define @t55 () (not (forall @t11 (or (not (forall @t42 (or @t54 (_ @t51 (_ @t14 @t40))))) @t53)))) % 0.40/0.65 (define @t56 () (_ tptp.ap @t8)) % 0.40/0.65 (define @t57 () (_ @t51 @t8)) % 0.40/0.65 (define @t58 () (not @t57)) % 0.40/0.65 (define @t59 () (not (forall @t28 (or @t58 @t54 (_ @t51 (_ @t56 @t24)))))) % 0.40/0.65 (define @t60 () (not (forall @t11 (or (not (_ tptp.var @t8)) @t57)))) % 0.40/0.65 (define @t61 () (forall (@list @t51 @t50) (or @t60 @t59 @t55 (_ @t51 @t50)))) % 0.40/0.65 (define @t62 () (@list @t38)) % 0.40/0.65 (define @t63 () (forall (@list @t2) (not (forall @t62 @t47)))) % 0.40/0.65 (define @t64 () (@var "Bound_variable_2910" tptp.term)) % 0.40/0.65 (define @t65 () (forall (@list @t2 @t38 @t64) (or @t35 @t34 @t23 @t47 (not (forall @t42 (or @t41 (_ @t38 (_ (_ tptp.sub @t64) @t40))))) (_ @t38 (_ tptp.lam @t64))))) % 0.40/0.65 (define @t66 () (_ (_ tptp.push @t8) @t16)) % 0.40/0.65 (define @t67 () (_ tptp.sub @t43)) % 0.40/0.65 (define @t68 () (_ @t67 @t66)) % 0.40/0.65 (define @t69 () (_ @t51 @t68)) % 0.40/0.65 (define @t70 () (= @t44 @t69)) % 0.40/0.65 (define @t71 () (forall @t45 @t70)) % 0.40/0.65 (define @t72 () (not @t71)) % 0.40/0.65 (define @t73 () (forall @t62 @t72)) % 0.40/0.65 (define @t74 () (not @t73)) % 0.40/0.65 (define @t75 () (@list @t51 @t8 @t16)) % 0.40/0.65 (define @t76 () (forall @t75 @t74)) % 0.40/0.65 (define @t77 () (_ tptp.comp tptp.sh)) % 0.40/0.65 (define @t78 () (@list @t8 @t16)) % 0.40/0.65 (define @t79 () (forall @t78 (= @t16 (_ @t77 @t66)))) % 0.40/0.65 (define @t80 () (@var "K" (-> tptp.term Bool))) % 0.40/0.65 (define @t81 () (forall (@list @t51 @t80 @t8 @t16 @t24) (or @t58 (_ @t80 (_ @t14 (_ @t39 @t16)))))) % 0.40/0.65 (define @t82 () (_ tptp.sub tptp.one)) % 0.40/0.65 (define @t83 () (forall @t78 (= @t8 (_ @t82 @t66)))) % 0.40/0.65 (define @t84 () (@var "Bound_variable_2605" tptp.term)) % 0.40/0.65 (define @t85 () (@var "Bound_variable_2603" tptp.term)) % 0.40/0.65 (define @t86 () (_ tptp.d2subst tptp.d_id)) % 0.40/0.65 (define @t87 () (_ tptp.d2term tptp.d_one)) % 0.40/0.65 (define @t88 () (@var "Bound_variable_3295" tptp.term)) % 0.40/0.65 (define @t89 () (forall (@list @t2 @t88) (or @t29 @t23 (_ (_ @t3 @t88) tptp.id)))) % 0.40/0.65 (define @t90 () (@var "Bound_variable_3232" tptp.term)) % 0.40/0.65 (define @t91 () (forall (@list @t2 @t90) (or @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t90) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t90)) tptp.id)))) % 0.40/0.65 (define @t92 () (@list @t16)) % 0.40/0.65 (define @t93 () (forall @t92 (= @t16 (_ @t17 tptp.id)))) % 0.40/0.65 (define @t94 () (forall @t92 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 0.40/0.65 (define @t95 () (and @t94 @t93)) % 0.40/0.65 (define @t96 () (_ (_ tptp.push tptp.one) tptp.sh)) % 0.40/0.65 (define @t97 () (_ tptp.sub @t24)) % 0.40/0.65 (define @t98 () (forall @t42 (not (forall @t22 (not (= @t5 (_ @t97 @t96))))))) % 0.40/0.65 (define @t99 () (@var "Bound_variable_2342" tptp.subst)) % 0.40/0.65 (define @t100 () (@var "Bound_variable_2340" tptp.term)) % 0.40/0.65 (define @t101 () (forall (@list @t51 @t100 @t99) (or @t59 @t55 (not (forall @t42 (or (not (_ tptp.var @t24)) (_ @t51 (_ @t97 @t99))))) (_ @t51 (_ (_ tptp.sub @t100) @t99))))) % 0.40/0.65 (define @t102 () (forall @t42 (not (forall @t22 (not (forall @t78 (= (_ @t97 @t66) @t19))))))) % 0.40/0.65 (define @t103 () (= tptp.pushprop_lem0 @t76)) % 0.40/0.65 (define @t104 () (@var "Bound_variable_3211" tptp.term)) % 0.40/0.65 (define @t105 () (forall (@list @t2 @t104) (or @t35 @t34 @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t104) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t104)) tptp.id)))) % 0.40/0.65 (define @t106 () (@var "Bound_variable_3046" tptp.term)) % 0.40/0.65 (define @t107 () (_ tptp.sub @t106)) % 0.40/0.65 (define @t108 () (forall (@list @t2 @t106) (or @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ @t107 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t107 @t96))) tptp.id)))) % 0.40/0.65 (define @t109 () (= @t8 @t24)) % 0.40/0.65 (define @t110 () (forall @t28 (or (not (= @t52 (_ tptp.lam @t24))) @t109))) % 0.40/0.65 (define @t111 () (@var "Bound_variable_2551" tptp.term)) % 0.40/0.65 (define @t112 () (@var "Bound_variable_2549" tptp.subst)) % 0.40/0.65 (define @t113 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 0.40/0.65 (define @t114 () (forall (@list @t4 @t113 @t112 @t111) (or @t21 (not (forall @t20 (= (_ (_ tptp.sub (_ (_ @t113 @t16) @t8)) @t13) (_ (_ @t113 @t18) @t15)))) (not (= @t6 (_ tptp.lam (_ (_ @t113 tptp.sh) tptp.one)))) (= (_ (_ @t4 @t112) @t111) (_ (_ @t113 @t112) @t111))))) % 0.40/0.65 (define @t115 () (@var "D" tptp.term)) % 0.40/0.65 (define @t116 () (@var "C" tptp.term)) % 0.40/0.65 (define @t117 () (not (= (_ @t26 @t116) (_ (_ tptp.ap (_ @t97 tptp.id)) @t115)))) % 0.40/0.65 (define @t118 () (@list @t8 @t24 @t116 @t115)) % 0.40/0.65 (define @t119 () (forall @t118 (or @t117 @t109))) % 0.40/0.65 (define @t120 () (not (= (_ @t56 @t116) (_ (_ tptp.ap @t24) @t115)))) % 0.40/0.65 (define @t121 () (forall @t118 (or @t120 @t109))) % 0.40/0.65 (define @t122 () (= @t116 @t115)) % 0.40/0.65 (define @t123 () (forall @t118 (or @t117 @t122))) % 0.40/0.65 (define @t124 () (forall @t118 (or @t120 @t122))) % 0.40/0.65 (define @t125 () (@var "Bound_variable_2822" tptp.term)) % 0.40/0.65 (define @t126 () (@var "Bound_variable_2820" tptp.term)) % 0.40/0.65 (define @t127 () (@var "Bound_variable_2140" tptp.term)) % 0.40/0.65 (define @t128 () (forall (@list @t51 @t127) (or @t60 @t59 (not (forall @t11 (or @t58 @t53))) (_ @t51 @t127)))) % 0.40/0.65 (define @t129 () (forall (@list @t51 @t38 @t8 @t16) (or @t58 @t72 (_ @t38 tptp.one)))) % 0.40/0.65 (define @t130 () (@var "Bound_variable_3001" tptp.term)) % 0.40/0.65 (define @t131 () (@var "Bound_variable_2999" tptp.term)) % 0.40/0.65 (define @t132 () (forall (@list @t2 @t131 @t130) (or @t35 @t34 @t29 (not (_ (_ @t3 @t131) tptp.id)) (not (_ (_ @t3 @t130) tptp.id)) (_ (_ @t3 (_ (_ tptp.ap @t131) @t130)) tptp.id)))) % 0.40/0.65 (define @t133 () (@var "Bound_variable_3171" tptp.term)) % 0.40/0.65 (define @t134 () (_ tptp.sub @t133)) % 0.40/0.65 (define @t135 () (@var "Bound_variable_3094" tptp.subst)) % 0.40/0.65 (define @t136 () (@var "Bound_variable_3090" tptp.subst)) % 0.40/0.65 (define @t137 () (_ (_ tptp.comp @t136) @t135)) % 0.40/0.65 (define @t138 () (@var "Bound_variable_3092" tptp.term)) % 0.40/0.65 (define @t139 () (_ (_ tptp.sub @t138) @t135)) % 0.40/0.65 (define @t140 () (@var "Bound_variable_3149" tptp.term)) % 0.40/0.65 (define @t141 () (_ tptp.sub @t140)) % 0.40/0.65 (define @t142 () (@var "Bound_variable_3076" tptp.subst)) % 0.40/0.65 (define @t143 () (@var "Bound_variable_3072" tptp.subst)) % 0.40/0.65 (define @t144 () (@var "Bound_variable_3074" tptp.term)) % 0.40/0.65 (define @t145 () (@list @t8 @t16 @t51 @t38)) % 0.40/0.65 (define @t146 () (lambda @t145 @t71)) % 0.40/0.65 (define @t147 () (= tptp.pushprop_p_and_p_prime @t146)) % 0.40/0.65 (define @t148 () (@var "DS2" tptp.d_subst)) % 0.40/0.65 (define @t149 () (@var "DS1" tptp.d_subst)) % 0.40/0.65 (define @t150 () (@var "DS" tptp.d_subst)) % 0.40/0.65 (define @t151 () (@list @t150)) % 0.40/0.65 (define @t152 () (@var "S" tptp.subst)) % 0.40/0.65 (define @t153 () (@var "DT2" tptp.d_term)) % 0.40/0.65 (define @t154 () (@var "DT1" tptp.d_term)) % 0.40/0.65 (define @t155 () (@var "DT" tptp.d_term)) % 0.40/0.65 (define @t156 () (@list @t155)) % 0.40/0.65 (define @t157 () (@var "T" tptp.term)) % 0.40/0.65 (define @t158 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t8) @t16) @t51) @t38)) % 0.40/0.65 (define @t159 () (exists @t62 @t158)) % 0.40/0.65 (define @t160 () (forall @t75 @t159)) % 0.40/0.65 (define @t161 () (= tptp.pushprop_lem0 @t160)) % 0.40/0.65 (define @t162 () (not @t161)) % 0.40/0.65 (define @t163 () (tptp.push @t8 @t16)) % 0.40/0.65 (define @t164 () (tptp.sub @t43 @t163)) % 0.40/0.65 (define @t165 () (_ @t51 @t164)) % 0.40/0.65 (define @t166 () (_ @t38 @t43)) % 0.40/0.65 (define @t167 () (forall @t45 (= @t166 @t165))) % 0.40/0.65 (define @t168 () (forall @t75 (not (forall @t62 (not @t167))))) % 0.40/0.65 (define @t169 () (_ (lambda @t145 @t167) @t8 @t16 @t51 @t38)) % 0.40/0.65 (define @t170 () (not @t169)) % 0.40/0.65 (define @t171 () (forall @t62 @t170)) % 0.40/0.65 (define @t172 () (not @t171)) % 0.40/0.65 (define @t173 () (forall @t75 @t172)) % 0.40/0.65 (define @t174 () (= @t168 @t173)) % 0.40/0.65 (define @t175 () (tptp.pushprop_p_and_p_prime @t8 @t16 @t51 @t38)) % 0.40/0.65 (define @t176 () (not @t175)) % 0.40/0.65 (define @t177 () (forall @t62 @t176)) % 0.40/0.65 (define @t178 () (not @t177)) % 0.40/0.65 (define @t179 () (forall @t75 @t178)) % 0.40/0.65 (define @t180 () (= tptp.pushprop_lem0 @t179)) % 0.40/0.65 (define @t181 () (not @t158)) % 0.40/0.65 (define @t182 () (forall @t62 @t181)) % 0.40/0.65 (define @t183 () (not @t182)) % 0.40/0.65 (assume @p1 (and (forall (@list @t157) (exists @t156 (= @t157 (_ tptp.d2term @t155)))) (forall @t156 (= @t155 tptp.d_one)) (forall (@list @t154 @t153) (=> (= (_ tptp.d2term @t154) (_ tptp.d2term @t153)) (= @t154 @t153))) (forall (@list @t152) (exists @t151 (= @t152 (_ tptp.d2subst @t150)))) (forall @t151 (= @t150 tptp.d_id)) (forall (@list @t149 @t148) (=> (= (_ tptp.d2subst @t149) (_ tptp.d2subst @t148)) (= @t149 @t148))) (= tptp.one @t87) (= (_ (_ tptp.ap @t87) @t87) @t87) (= (_ tptp.lam @t87) @t87) (= (_ (_ tptp.sub @t87) @t86) @t87) (= tptp.id @t86) (= tptp.sh @t86) (= (_ (_ tptp.push @t87) @t86) @t86) (= (_ (_ tptp.comp @t86) @t86) @t86) (= (_ (_ (_ (_ tptp.hoasap @t86) @t87) @t86) @t87) @t87) (= tptp.hoaslam (lambda (@list (@var "Bound_variable_4913" tptp.subst) (@var "Bound_variable_4915" (-> tptp.subst tptp.term tptp.term))) @t87)) (= tptp.hoasinduction_p_and_p_prime (lambda (@list @t2 @t38) @t46)) @t147 (not (_ tptp.var @t87)) (= tptp.pushprop_lem1v2 @t129) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t28 (or (not (= (_ @t14 tptp.sh) (_ @t97 tptp.sh))) @t109))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t101) (= tptp.hoasinduction_lem3v2_f @t102) tptp.axvarshift (= tptp.hoasapinj2 @t123) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t119) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t83 (=> @t79 (=> @t93 (=> @t128 @t101))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t102) (= tptp.hoasinduction_lthm (=> @t61 (=> @t132 (=> @t105 @t36)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t63 (=> @t61 (=> @t49 (=> @t48 @t89))))) (= tptp.hoaslaminj @t114) (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t133) (or (not (forall (@list @t4 @t140) (or @t12 @t7 (not (forall (@list @t143 @t144 @t142) (= (_ (_ tptp.sub (_ (_ @t4 @t143) @t144)) @t142) (_ (_ tptp.sub (_ @t141 (_ (_ tptp.push @t144) @t143))) @t142)))) (not (forall (@list @t136 @t138 @t135) (= (_ (_ @t4 @t137) @t139) (_ @t141 (_ (_ tptp.push @t139) @t137)))))))) (not (forall @t42 (or @t27 (_ (_ @t3 (_ @t134 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t134 @t96))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t108) (= tptp.hoasinduction_lem3 @t105) (= tptp.hoasinduction_lem2 @t132) (= tptp.termmset_lthm (=> @t49 @t49)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t83 @t129)) tptp.hoasapnotvar (= tptp.hoasinduction_lem0 @t63) (= tptp.hoasinduction @t36) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t98) tptp.ulamvarind (= tptp.induction @t128) (= tptp.hoasinduction_lem3a_lthm (=> @t49 (=> @t108 @t91))) tptp.termmset_gthm (= tptp.hoasinduction_lem3aa @t108) 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 @t126 @t125) (or @t35 @t34 @t29 @t47 (not (_ @t38 @t126)) (not (_ @t38 @t125)) (_ @t38 (_ (_ tptp.ap @t126) @t125))))) tptp.pushprop_lthm (= tptp.apinj2 @t124) (= tptp.apinj1 @t121) (= tptp.hoasapinj2_lthm (=> @t124 @t123)) (= tptp.hoasinduction_lem3v2a @t48) (= tptp.hoasapinj1_lthm (=> @t49 (=> @t121 @t119))) (= tptp.hoaslaminj_lthm (=> @t83 (=> @t79 (=> @t110 @t114)))) (= tptp.axvarcons @t83) (= tptp.axscons (forall @t92 (= @t16 (_ (_ tptp.push (_ @t82 @t16)) (_ @t77 @t16))))) tptp.hoasinduction_lem2v2_gthm (= tptp.axidr @t93) (= tptp.pushprop_lem1 @t81) (= tptp.laminj @t110) (= tptp.hoasinduction_lem3_lthm (=> @t49 (=> @t108 @t105))) @t103 tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t102 (=> @t49 @t48))) tptp.hoasinduction_lem2_lthm tptp.hoasapinj2_gthm tptp.hoasinduction_lem1_lthm (not tptp.lamnotap) tptp.hoasapinj1_gthm tptp.hoaslamnotvar (= tptp.axidl @t94) tptp.hoaslaminj_gthm (= tptp.induction2_lthm (=> @t49 (=> @t101 @t61))) (= tptp.hoasinduction_lem0_lthm @t63) (= tptp.substmonoid_lthm (=> @t94 (=> @t93 @t95))) tptp.pushprop tptp.hoasinduction_lem3_gthm tptp.hoasinduction_lem2_gthm (= tptp.hoasinduction_lem3b @t98) (= tptp.substmonoid @t95) tptp.lamnotvar (= tptp.hoasinduction_lem3a @t91) tptp.hoasinduction_lem1_gthm (= tptp.hoasinduction_no_psi_cond @t89) tptp.induction2_gthm tptp.pushprop_lem2v2_lthm (not (_ (_ (_ tptp.hoasvar @t86) @t87) @t86)) (= tptp.hoaslamnotap (forall (@list @t4 @t85 @t84) (or @t21 (not (= @t6 (_ (_ tptp.ap (_ (_ tptp.sub @t85) tptp.id)) @t84)))))) tptp.substmonoid_gthm tptp.ulamvarsh (= tptp.induction2 @t61) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t83 (=> @t79 @t81))) (= tptp.hoasinduction_lem3v2 @t65) (= tptp.axshiftcons @t79) (= tptp.termmset @t49) (= tptp.pushprop_lem0_lthm @t76) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t49 @t65)) (= tptp.axvarid @t49) (= tptp.hoasinduction_lthm_3 (=> @t63 (=> @t61 (=> @t49 (=> @t48 @t36))))))) % 0.40/0.65 (assume @p2 @t162) % 0.40/0.65 (assume @p3 true) % 0.40/0.65 (step @p4 :rule evaluate :args ((not true))) % 0.40/0.65 (step @p5 :rule eq-refl :args (@t168)) % 0.40/0.65 (step @p6 :rule beta-reduce :args ((= @t169 @t167))) % 0.40/0.65 (step @p7 :rule cong :premises (@p6) :args (@t170)) % 0.40/0.65 (step @p8 :rule cong :premises (@p7) :args (@t171)) % 0.40/0.65 (step @p9 :rule cong :premises (@p8) :args (@t172)) % 0.40/0.65 (step @p10 :rule cong :premises (@p9) :args (@t173)) % 0.40/0.65 (step @p11 :rule refl :args (@t168)) % 0.40/0.65 (step @p12 :rule cong :premises (@p11 @p10) :args (@t174)) % 0.40/0.65 (step @p13 :rule trans :premises (@p12 @p5)) % 0.40/0.65 (step @p14 :rule cong :premises (@p13) :args ((not @t174))) % 0.40/0.65 (step @p15 :rule trans :premises (@p14 @p4)) % 0.40/0.65 (step @p16 :rule refl :args (@t38)) % 0.40/0.65 (step @p17 :rule refl :args (@t51)) % 0.40/0.65 (step @p18 :rule refl :args (@t16)) % 0.40/0.65 (step @p19 :rule refl :args (@t8)) % 0.40/0.65 (step @p20 :rule refl :args ((_ @t51 @t68))) % 0.40/0.65 (step @p21 :rule refl :args ((tptp.sub @t43 @t66))) % 0.40/0.65 (step @p22 :rule refl :args (@t163)) % 0.40/0.65 (step @p23 :rule refl :args (@t43)) % 0.40/0.65 (step @p24 :rule cong :premises (@p23 @p22) :args (@t164)) % 0.40/0.65 (step @p25 :rule trans :premises (@p24 @p21)) % 0.40/0.65 (step @p26 :rule cong :premises (@p25) :args (@t165)) % 0.40/0.65 (step @p27 :rule trans :premises (@p26 @p20)) % 0.40/0.65 (step @p28 :rule refl :args (@t51)) % 0.40/0.65 (step @p29 :rule ho_cong :premises (@p28 @p25)) % 0.40/0.65 (step @p30 :rule cong :premises (@p29 @p27) :args ((= (_ @t51 @t164) @t165))) % 0.40/0.65 (step @p31 :rule symm :premises (@p30)) % 0.40/0.65 (step @p32 :rule refl :args (@t69)) % 0.40/0.65 (step @p33 :rule eq_resolve :premises (@p32 @p31)) % 0.40/0.65 (step @p34 :rule refl :args (@t67)) % 0.40/0.65 (step @p35 :rule ho_cong :premises (@p34 @p22)) % 0.40/0.65 (step @p36 :rule cong :premises (@p35 @p25) :args ((= (_ @t67 @t163) @t164))) % 0.40/0.65 (step @p37 :rule symm :premises (@p36)) % 0.40/0.65 (step @p38 :rule refl :args (@t68)) % 0.40/0.65 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 0.40/0.65 (step @p40 :rule refl :args (@t66)) % 0.40/0.65 (step @p41 :rule cong :premises (@p40 @p22) :args ((= @t66 @t163))) % 0.40/0.65 (step @p42 :rule symm :premises (@p41)) % 0.40/0.65 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.40/0.65 (step @p44 :rule ho_cong :premises (@p34 @p43)) % 0.40/0.65 (step @p45 :rule trans :premises (@p44 @p39)) % 0.40/0.65 (step @p46 :rule ho_cong :premises (@p28 @p45)) % 0.40/0.65 (step @p47 :rule trans :premises (@p46 @p33)) % 0.40/0.65 (step @p48 :rule refl :args (@t166)) % 0.40/0.65 (step @p49 :rule refl :args (@t44)) % 0.40/0.65 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t44 @t166))) % 0.40/0.65 (step @p51 :rule symm :premises (@p50)) % 0.40/0.65 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.40/0.65 (step @p53 :rule cong :premises (@p52 @p47) :args (@t70)) % 0.40/0.65 (step @p54 :rule cong :premises (@p53) :args (@t71)) % 0.40/0.65 (step @p55 :rule cong :premises (@p54) :args (@t146)) % 0.40/0.65 (step @p56 :rule refl :args (tptp.pushprop_p_and_p_prime)) % 0.40/0.65 (step @p57 :rule cong :premises (@p56 @p55) :args (@t147)) % 0.40/0.65 (step @p58 :rule and_elim :premises (@p1) :args (17)) % 0.40/0.65 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.40/0.65 (step @p60 :rule ho_cong :premises (@p59 @p19 @p18 @p17 @p16)) % 0.40/0.65 (step @p61 :rule cong :premises (@p60) :args (@t176)) % 0.40/0.65 (step @p62 :rule cong :premises (@p61) :args (@t177)) % 0.40/0.65 (step @p63 :rule cong :premises (@p62) :args (@t178)) % 0.40/0.65 (step @p64 :rule cong :premises (@p63) :args (@t179)) % 0.40/0.65 (step @p65 :rule cong :premises (@p54) :args (@t72)) % 0.40/0.65 (step @p66 :rule cong :premises (@p65) :args (@t73)) % 0.40/0.65 (step @p67 :rule cong :premises (@p66) :args (@t74)) % 0.40/0.65 (step @p68 :rule cong :premises (@p67) :args (@t76)) % 0.40/0.65 (step @p69 :rule refl :args (tptp.pushprop_lem0)) % 0.40/0.65 (step @p70 :rule cong :premises (@p69 @p68) :args (@t103)) % 0.40/0.65 (step @p71 :rule and_elim :premises (@p1) :args (86)) % 0.40/0.65 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 0.40/0.65 (step @p73 :rule cong :premises (@p72 @p64) :args (@t180)) % 0.40/0.65 (step @p74 :rule cong :premises (@p73) :args ((not @t180))) % 0.40/0.65 (step @p75 :rule trans :premises (@p74 @p15)) % 0.40/0.65 (step @p76 :rule refl :args (@t175)) % 0.40/0.65 (step @p77 :rule refl :args (@t158)) % 0.40/0.65 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t158 @t175))) % 0.40/0.65 (step @p79 :rule symm :premises (@p78)) % 0.40/0.65 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.40/0.65 (step @p81 :rule cong :premises (@p80) :args (@t181)) % 0.40/0.65 (step @p82 :rule cong :premises (@p81) :args (@t182)) % 0.40/0.65 (step @p83 :rule cong :premises (@p82) :args (@t183)) % 0.40/0.65 (step @p84 :rule exists-elim :args ((= @t159 @t183))) % 0.40/0.65 (step @p85 :rule trans :premises (@p84 @p83)) % 0.40/0.65 (step @p86 :rule cong :premises (@p85) :args (@t160)) % 0.40/0.65 (step @p87 :rule cong :premises (@p69 @p86) :args (@t161)) % 0.40/0.65 (step @p88 :rule cong :premises (@p87) :args (@t162)) % 0.40/0.65 (step @p89 :rule eq_resolve :premises (@p2 @p88)) % 0.40/0.65 (step @p90 false :rule eq_resolve :premises (@p89 @p75)) % 0.40/0.65 ) % 0.40/0.65 % SZS output end Proof % 0.40/0.65 % cvc5 exiting %------------------------------------------------------------------------------