%------------------------------------------------------------------------------ % 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 09:07:15 AM UTC 2026 % Result : Theorem 0.39s 0.68s % Output : Proof 0.39s % 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. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n014.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 23:02:28 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.55 %----Proving TH0 % 0.39/0.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.68 % SZS status Theorem % 0.39/0.68 % SZS output start Proof % 0.39/0.68 ( % 0.39/0.68 (declare-sort tptp.term 0) % 0.39/0.68 (declare-sort tptp.subst 0) % 0.39/0.68 (declare-sort tptp.d_term 0) % 0.39/0.68 (declare-sort tptp.d_subst 0) % 0.39/0.68 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 0.39/0.68 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 0.39/0.68 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 0.39/0.68 (declare-const tptp.pushprop_lem1v2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.39/0.68 (declare-const tptp.axmap Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.39/0.68 (declare-const tptp.shinj Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.39/0.68 (declare-const tptp.induction2lem Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.39/0.68 (declare-const tptp.axvarshift Bool) % 0.39/0.68 (declare-const tptp.hoasapinj2 Bool) % 0.39/0.68 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasapinj1 Bool) % 0.39/0.68 (declare-const tptp.ulamvar1 Bool) % 0.39/0.68 (declare-const tptp.induction2lem_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.39/0.68 (declare-const tptp.apnotvar Bool) % 0.39/0.68 (declare-const tptp.pushprop_lthm_orig Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.39/0.68 (declare-const tptp.hoaslaminj Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.39/0.68 (declare-const tptp.induction2lem_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2 Bool) % 0.39/0.68 (declare-const tptp.termmset_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1 Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasapnotvar Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem0 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_gthm Bool) % 0.39/0.68 (declare-const tptp.axapp Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.39/0.68 (declare-const tptp.ulamvarind Bool) % 0.39/0.68 (declare-const tptp.induction Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.39/0.68 (declare-const tptp.termmset_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem2v2 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.39/0.68 (declare-const tptp.axclos Bool) % 0.39/0.68 (declare-const tptp.axassoc Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_lthm Bool) % 0.39/0.68 (declare-const tptp.apinj2 Bool) % 0.39/0.68 (declare-const tptp.apinj1 Bool) % 0.39/0.68 (declare-const tptp.hoasapinj2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.39/0.68 (declare-const tptp.hoasapinj1_lthm Bool) % 0.39/0.68 (declare-const tptp.hoaslaminj_lthm Bool) % 0.39/0.68 (declare-const tptp.axvarcons Bool) % 0.39/0.68 (declare-const tptp.axscons Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.39/0.68 (declare-const tptp.d_one tptp.d_term) % 0.39/0.68 (declare-const tptp.hoaslamnotap Bool) % 0.39/0.68 (declare-const tptp.ulamvarsh Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem3v2 Bool) % 0.39/0.68 (declare-const tptp.axshiftcons Bool) % 0.39/0.68 (declare-const tptp.id tptp.subst) % 0.39/0.68 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 0.39/0.68 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.39/0.68 (declare-const tptp.one tptp.term) % 0.39/0.68 (declare-const tptp.substmonoid_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.39/0.68 (declare-const tptp.sh tptp.subst) % 0.39/0.68 (declare-const tptp.termmset Bool) % 0.39/0.68 (declare-const tptp.induction2 Bool) % 0.39/0.68 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 0.39/0.68 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.39/0.68 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.39/0.68 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.39/0.68 (declare-const tptp.axvarid Bool) % 0.39/0.68 (declare-const tptp.d_id tptp.d_subst) % 0.39/0.68 (declare-const tptp.var (-> tptp.term Bool)) % 0.39/0.68 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 0.39/0.68 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.39/0.68 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.39/0.68 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.39/0.68 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.39/0.68 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 0.39/0.68 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.39/0.68 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.39/0.68 (declare-const tptp.induction2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3a Bool) % 0.39/0.68 (declare-const tptp.lamnotvar Bool) % 0.39/0.68 (declare-const tptp.substmonoid Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3b Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.39/0.68 (declare-const tptp.pushprop Bool) % 0.39/0.68 (declare-const tptp.substmonoid_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.39/0.68 (declare-const tptp.induction2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoaslaminj_gthm Bool) % 0.39/0.68 (declare-const tptp.axidl Bool) % 0.39/0.68 (declare-const tptp.hoaslamnotvar Bool) % 0.39/0.68 (declare-const tptp.hoasapinj1_gthm Bool) % 0.39/0.68 (declare-const tptp.lamnotap Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasapinj2_gthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.39/0.68 (declare-const tptp.axabs Bool) % 0.39/0.68 (declare-const tptp.pushprop_gthm Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem0 Bool) % 0.39/0.68 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.39/0.68 (declare-const tptp.laminj Bool) % 0.39/0.68 (declare-const tptp.pushprop_lem1 Bool) % 0.39/0.68 (declare-const tptp.axidr Bool) % 0.39/0.68 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 0.39/0.68 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.39/0.68 (define @t3 () (_ @t2 tptp.id)) % 0.39/0.68 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.68 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 0.39/0.68 (define @t6 () (_ tptp.lam @t5)) % 0.39/0.68 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 0.39/0.68 (define @t8 () (@var "A" tptp.term)) % 0.39/0.68 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 0.39/0.68 (define @t10 () (not @t9)) % 0.39/0.68 (define @t11 () (@list @t8)) % 0.39/0.68 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 0.39/0.68 (define @t13 () (@var "N" tptp.subst)) % 0.39/0.68 (define @t14 () (_ tptp.sub @t8)) % 0.39/0.68 (define @t15 () (_ @t14 @t13)) % 0.39/0.68 (define @t16 () (@var "M" tptp.subst)) % 0.39/0.68 (define @t17 () (_ tptp.comp @t16)) % 0.39/0.68 (define @t18 () (_ @t17 @t13)) % 0.39/0.68 (define @t19 () (_ (_ @t4 @t16) @t8)) % 0.39/0.68 (define @t20 () (@list @t16 @t8 @t13)) % 0.39/0.68 (define @t21 () (not (forall @t20 (= (_ (_ tptp.sub @t19) @t13) (_ (_ @t4 @t18) @t15))))) % 0.39/0.68 (define @t22 () (@list @t4)) % 0.39/0.68 (define @t23 () (not (forall @t22 (or @t21 @t12 @t7)))) % 0.39/0.68 (define @t24 () (@var "B" tptp.term)) % 0.39/0.68 (define @t25 () (_ @t14 tptp.id)) % 0.39/0.68 (define @t26 () (_ tptp.ap @t25)) % 0.39/0.68 (define @t27 () (not (_ (_ @t3 @t24) tptp.id))) % 0.39/0.68 (define @t28 () (@list @t8 @t24)) % 0.39/0.68 (define @t29 () (not (forall @t28 (or @t10 @t27 (_ (_ @t3 (_ @t26 @t24)) tptp.id))))) % 0.39/0.68 (define @t30 () (@var "K" tptp.subst)) % 0.39/0.68 (define @t31 () (_ (_ (_ @t2 @t16) @t8) (_ (_ tptp.comp @t30) @t13))) % 0.39/0.68 (define @t32 () (_ (_ (_ @t2 (_ @t17 @t30)) (_ @t14 @t30)) @t13)) % 0.39/0.68 (define @t33 () (@list @t16 @t8 @t13 @t30)) % 0.39/0.68 (define @t34 () (not (forall @t33 (or (not @t32) @t31)))) % 0.39/0.68 (define @t35 () (not (forall @t33 (or (not @t31) @t32)))) % 0.39/0.68 (define @t36 () (forall (@list @t2 @t1) (or @t35 @t34 (not (forall @t11 (or (not (_ tptp.var @t25)) @t9))) @t29 @t23 (_ (_ @t3 @t1) tptp.id)))) % 0.39/0.68 (define @t37 () (@var "Bound_variable_2931" tptp.term)) % 0.39/0.68 (define @t38 () (@var "Q" (-> tptp.term Bool))) % 0.39/0.68 (define @t39 () (_ tptp.push @t24)) % 0.39/0.68 (define @t40 () (_ @t39 tptp.id)) % 0.39/0.68 (define @t41 () (_ @t38 @t24)) % 0.39/0.68 (define @t42 () (not @t41)) % 0.39/0.68 (define @t43 () (@list @t24)) % 0.39/0.68 (define @t44 () (@var "X" tptp.term)) % 0.39/0.68 (define @t45 () (_ @t38 @t44)) % 0.39/0.68 (define @t46 () (@list @t44)) % 0.39/0.68 (define @t47 () (forall @t46 (= @t45 (_ (_ @t3 @t44) tptp.id)))) % 0.39/0.68 (define @t48 () (not @t47)) % 0.39/0.68 (define @t49 () (forall (@list @t2 @t38 @t37) (or @t23 @t48 (not (forall @t43 (or @t42 (_ @t38 (_ (_ tptp.sub @t37) @t40))))) (_ @t38 (_ tptp.lam @t37))))) % 0.39/0.68 (define @t50 () (forall @t11 (= @t8 @t25))) % 0.39/0.68 (define @t51 () (@var "Bound_variable_2367" tptp.term)) % 0.39/0.68 (define @t52 () (@var "P" (-> tptp.term Bool))) % 0.39/0.68 (define @t53 () (_ tptp.lam @t8)) % 0.39/0.68 (define @t54 () (_ @t52 @t53)) % 0.39/0.68 (define @t55 () (not (_ @t52 @t24))) % 0.39/0.68 (define @t56 () (not (forall @t11 (or (not (forall @t43 (or @t55 (_ @t52 (_ @t14 @t40))))) @t54)))) % 0.39/0.68 (define @t57 () (_ tptp.ap @t8)) % 0.39/0.68 (define @t58 () (_ @t52 @t8)) % 0.39/0.68 (define @t59 () (not @t58)) % 0.39/0.68 (define @t60 () (not (forall @t28 (or @t59 @t55 (_ @t52 (_ @t57 @t24)))))) % 0.39/0.68 (define @t61 () (not (forall @t11 (or (not (_ tptp.var @t8)) @t58)))) % 0.39/0.68 (define @t62 () (forall (@list @t52 @t51) (or @t61 @t60 @t56 (_ @t52 @t51)))) % 0.39/0.68 (define @t63 () (@list @t38)) % 0.39/0.68 (define @t64 () (forall (@list @t2) (not (forall @t63 @t48)))) % 0.39/0.68 (define @t65 () (@var "Bound_variable_2910" tptp.term)) % 0.39/0.68 (define @t66 () (forall (@list @t2 @t38 @t65) (or @t35 @t34 @t23 @t48 (not (forall @t43 (or @t42 (_ @t38 (_ (_ tptp.sub @t65) @t40))))) (_ @t38 (_ tptp.lam @t65))))) % 0.39/0.68 (define @t67 () (_ (_ tptp.push @t8) @t16)) % 0.39/0.68 (define @t68 () (_ tptp.sub @t44)) % 0.39/0.68 (define @t69 () (_ @t68 @t67)) % 0.39/0.68 (define @t70 () (_ @t52 @t69)) % 0.39/0.68 (define @t71 () (= @t45 @t70)) % 0.39/0.68 (define @t72 () (forall @t46 @t71)) % 0.39/0.68 (define @t73 () (not @t72)) % 0.39/0.68 (define @t74 () (forall (@list @t52 @t8 @t16) (not (forall @t63 @t73)))) % 0.39/0.68 (define @t75 () (_ tptp.comp tptp.sh)) % 0.39/0.68 (define @t76 () (@list @t8 @t16)) % 0.39/0.68 (define @t77 () (forall @t76 (= @t16 (_ @t75 @t67)))) % 0.39/0.68 (define @t78 () (@var "K" (-> tptp.term Bool))) % 0.39/0.68 (define @t79 () (forall (@list @t52 @t78 @t8 @t16 @t24) (or @t59 (_ @t78 (_ @t14 (_ @t39 @t16)))))) % 0.39/0.68 (define @t80 () (_ tptp.sub tptp.one)) % 0.39/0.68 (define @t81 () (forall @t76 (= @t8 (_ @t80 @t67)))) % 0.39/0.68 (define @t82 () (@var "Bound_variable_2605" tptp.term)) % 0.39/0.68 (define @t83 () (@var "Bound_variable_2603" tptp.term)) % 0.39/0.68 (define @t84 () (_ tptp.d2subst tptp.d_id)) % 0.39/0.68 (define @t85 () (_ tptp.d2term tptp.d_one)) % 0.39/0.68 (define @t86 () (@var "Bound_variable_3295" tptp.term)) % 0.39/0.68 (define @t87 () (forall (@list @t2 @t86) (or @t29 @t23 (_ (_ @t3 @t86) tptp.id)))) % 0.39/0.68 (define @t88 () (@var "Bound_variable_3232" tptp.term)) % 0.39/0.68 (define @t89 () (forall (@list @t2 @t88) (or @t23 (not (forall @t43 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t88) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t88)) tptp.id)))) % 0.39/0.68 (define @t90 () (@list @t16)) % 0.39/0.68 (define @t91 () (forall @t90 (= @t16 (_ @t17 tptp.id)))) % 0.39/0.68 (define @t92 () (forall @t90 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 0.39/0.68 (define @t93 () (and @t92 @t91)) % 0.39/0.68 (define @t94 () (_ (_ tptp.push tptp.one) tptp.sh)) % 0.39/0.68 (define @t95 () (_ tptp.sub @t24)) % 0.39/0.68 (define @t96 () (forall @t43 (not (forall @t22 (not (= @t5 (_ @t95 @t94))))))) % 0.39/0.68 (define @t97 () (@var "Bound_variable_2342" tptp.subst)) % 0.39/0.68 (define @t98 () (@var "Bound_variable_2340" tptp.term)) % 0.39/0.68 (define @t99 () (_ tptp.var @t24)) % 0.39/0.68 (define @t100 () (not @t99)) % 0.39/0.68 (define @t101 () (forall (@list @t52 @t98 @t97) (or @t60 @t56 (not (forall @t43 (or @t100 (_ @t52 (_ @t95 @t97))))) (_ @t52 (_ (_ tptp.sub @t98) @t97))))) % 0.39/0.68 (define @t102 () (_ @t95 @t67)) % 0.39/0.68 (define @t103 () (forall @t43 (not (forall @t22 (not (forall @t76 (= @t102 @t19))))))) % 0.39/0.68 (define @t104 () (@var "Bound_variable_3211" tptp.term)) % 0.39/0.68 (define @t105 () (forall (@list @t2 @t104) (or @t35 @t34 @t23 (not (forall @t43 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t104) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t104)) tptp.id)))) % 0.39/0.68 (define @t106 () (@var "Bound_variable_3046" tptp.term)) % 0.39/0.68 (define @t107 () (_ tptp.sub @t106)) % 0.39/0.68 (define @t108 () (forall (@list @t2 @t106) (or @t23 (not (forall @t43 (or @t27 (_ (_ @t3 (_ @t107 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t107 @t94))) tptp.id)))) % 0.39/0.68 (define @t109 () (= @t8 @t24)) % 0.39/0.68 (define @t110 () (forall @t28 (or (not (= @t53 (_ tptp.lam @t24))) @t109))) % 0.39/0.68 (define @t111 () (@var "Bound_variable_2551" tptp.term)) % 0.39/0.68 (define @t112 () (@var "Bound_variable_2549" tptp.subst)) % 0.39/0.68 (define @t113 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 0.39/0.68 (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))))) % 0.39/0.68 (define @t115 () (@var "D" tptp.term)) % 0.39/0.68 (define @t116 () (@var "C" tptp.term)) % 0.39/0.68 (define @t117 () (not (= (_ @t26 @t116) (_ (_ tptp.ap (_ @t95 tptp.id)) @t115)))) % 0.39/0.68 (define @t118 () (@list @t8 @t24 @t116 @t115)) % 0.39/0.68 (define @t119 () (forall @t118 (or @t117 @t109))) % 0.39/0.68 (define @t120 () (not (= (_ @t57 @t116) (_ (_ tptp.ap @t24) @t115)))) % 0.39/0.68 (define @t121 () (forall @t118 (or @t120 @t109))) % 0.39/0.68 (define @t122 () (= @t116 @t115)) % 0.39/0.68 (define @t123 () (forall @t118 (or @t117 @t122))) % 0.39/0.68 (define @t124 () (forall @t118 (or @t120 @t122))) % 0.39/0.68 (define @t125 () (@var "Bound_variable_2822" tptp.term)) % 0.39/0.68 (define @t126 () (@var "Bound_variable_2820" tptp.term)) % 0.39/0.68 (define @t127 () (@var "Bound_variable_2140" tptp.term)) % 0.39/0.68 (define @t128 () (forall (@list @t52 @t127) (or @t61 @t60 (not (forall @t11 (or @t59 @t54))) (_ @t52 @t127)))) % 0.39/0.68 (define @t129 () (@list @t52 @t38 @t8 @t16)) % 0.39/0.68 (define @t130 () (forall @t129 (or @t59 @t73 (_ @t38 tptp.one)))) % 0.39/0.68 (define @t131 () (@var "Bound_variable_3001" tptp.term)) % 0.39/0.68 (define @t132 () (@var "Bound_variable_2999" tptp.term)) % 0.39/0.68 (define @t133 () (forall (@list @t2 @t132 @t131) (or @t35 @t34 @t29 (not (_ (_ @t3 @t132) tptp.id)) (not (_ (_ @t3 @t131) tptp.id)) (_ (_ @t3 (_ (_ tptp.ap @t132) @t131)) tptp.id)))) % 0.39/0.68 (define @t134 () (@var "Bound_variable_3171" tptp.term)) % 0.39/0.68 (define @t135 () (_ tptp.sub @t134)) % 0.39/0.68 (define @t136 () (@var "Bound_variable_3094" tptp.subst)) % 0.39/0.68 (define @t137 () (@var "Bound_variable_3090" tptp.subst)) % 0.39/0.68 (define @t138 () (_ (_ tptp.comp @t137) @t136)) % 0.39/0.68 (define @t139 () (@var "Bound_variable_3092" tptp.term)) % 0.39/0.68 (define @t140 () (_ (_ tptp.sub @t139) @t136)) % 0.39/0.68 (define @t141 () (@var "Bound_variable_3149" tptp.term)) % 0.39/0.68 (define @t142 () (_ tptp.sub @t141)) % 0.39/0.68 (define @t143 () (@var "Bound_variable_3076" tptp.subst)) % 0.39/0.68 (define @t144 () (@var "Bound_variable_3072" tptp.subst)) % 0.39/0.68 (define @t145 () (@var "Bound_variable_3074" tptp.term)) % 0.39/0.68 (define @t146 () (@list @t8 @t16 @t52 @t38)) % 0.39/0.68 (define @t147 () (lambda @t146 @t72)) % 0.39/0.68 (define @t148 () (= tptp.pushprop_p_and_p_prime @t147)) % 0.39/0.68 (define @t149 () (@var "DS2" tptp.d_subst)) % 0.39/0.68 (define @t150 () (@var "DS1" tptp.d_subst)) % 0.39/0.68 (define @t151 () (@var "DS" tptp.d_subst)) % 0.39/0.68 (define @t152 () (@list @t151)) % 0.39/0.68 (define @t153 () (@var "S" tptp.subst)) % 0.39/0.68 (define @t154 () (@var "DT2" tptp.d_term)) % 0.39/0.68 (define @t155 () (@var "DT1" tptp.d_term)) % 0.39/0.68 (define @t156 () (@var "DT" tptp.d_term)) % 0.39/0.68 (define @t157 () (@list @t156)) % 0.39/0.68 (define @t158 () (@var "T" tptp.term)) % 0.39/0.68 (define @t159 () (_ @t52 @t102)) % 0.39/0.68 (define @t160 () (forall @t43 (=> @t99 @t159))) % 0.39/0.68 (define @t161 () (forall @t43 (=> @t99 @t41))) % 0.39/0.68 (define @t162 () (=> @t161 @t160)) % 0.39/0.68 (define @t163 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t8) @t16) @t52) @t38)) % 0.39/0.68 (define @t164 () (=> @t163 @t162)) % 0.39/0.68 (define @t165 () (forall @t129 @t164)) % 0.39/0.68 (define @t166 () (= tptp.pushprop_lem3v2 @t165)) % 0.39/0.68 (define @t167 () (not @t166)) % 0.39/0.68 (define @t168 () (tptp.push @t8 @t16)) % 0.39/0.68 (define @t169 () (@var "BOUND_VARIABLE_9039" tptp.term)) % 0.39/0.68 (define @t170 () (_ @t52 (tptp.sub @t169 @t168))) % 0.39/0.68 (define @t171 () (not (tptp.var @t169))) % 0.39/0.68 (define @t172 () (_ @t38 @t24)) % 0.39/0.68 (define @t173 () (tptp.var @t24)) % 0.39/0.68 (define @t174 () (not @t173)) % 0.39/0.68 (define @t175 () (forall @t43 (or @t174 @t172))) % 0.39/0.68 (define @t176 () (not @t175)) % 0.39/0.68 (define @t177 () (tptp.sub @t44 @t168)) % 0.39/0.68 (define @t178 () (_ @t52 @t177)) % 0.39/0.68 (define @t179 () (_ @t38 @t44)) % 0.39/0.68 (define @t180 () (forall @t46 (= @t179 @t178))) % 0.39/0.68 (define @t181 () (_ (lambda @t146 @t180) @t8 @t16 @t52 @t38)) % 0.39/0.68 (define @t182 () (not @t181)) % 0.39/0.68 (define @t183 () (or @t182 @t176 @t171 @t170)) % 0.39/0.68 (define @t184 () (@list @t52 @t38 @t8 @t16 @t169)) % 0.39/0.68 (define @t185 () (forall @t184 @t183)) % 0.39/0.68 (define @t186 () (tptp.pushprop_p_and_p_prime @t8 @t16 @t52 @t38)) % 0.39/0.68 (define @t187 () (not @t186)) % 0.39/0.68 (define @t188 () (or @t187 @t176 @t171 @t170)) % 0.39/0.68 (define @t189 () (forall @t184 @t188)) % 0.39/0.68 (define @t190 () (= tptp.pushprop_lem3v2 @t189)) % 0.39/0.68 (define @t191 () (or @t171 @t170)) % 0.39/0.68 (define @t192 () (or @t187 @t176 @t191)) % 0.39/0.68 (define @t193 () (forall @t184 @t192)) % 0.39/0.68 (define @t194 () (@list @t169)) % 0.39/0.68 (define @t195 () (forall @t194 @t192)) % 0.39/0.68 (define @t196 () (forall @t194 @t191)) % 0.39/0.68 (define @t197 () (or @t187 @t176 @t196)) % 0.39/0.68 (define @t198 () (tptp.sub @t24 @t168)) % 0.39/0.68 (define @t199 () (_ @t52 @t198)) % 0.39/0.68 (define @t200 () (forall @t43 (or @t174 @t199))) % 0.39/0.68 (define @t201 () (not @t163)) % 0.39/0.68 (define @t202 () (or @t201 @t176 @t200)) % 0.39/0.68 (define @t203 () (=> @t175 @t200)) % 0.39/0.68 (define @t204 () (or @t100 @t159)) % 0.39/0.68 (define @t205 () (or @t100 @t41)) % 0.39/0.68 (define @t206 () (forall @t184 (or (not @t180) @t176 @t171 @t170))) % 0.39/0.68 (define @t207 () (@quantifiers_skolemize @t206 4)) % 0.39/0.68 (define @t208 () (tptp.var @t207)) % 0.39/0.68 (define @t209 () (tptp.push (@quantifiers_skolemize @t206 2) (@quantifiers_skolemize @t206 3))) % 0.39/0.68 (define @t210 () (@quantifiers_skolemize @t206 0)) % 0.39/0.68 (define @t211 () (_ @t210 (tptp.sub @t207 @t209))) % 0.39/0.68 (define @t212 () (not @t208)) % 0.39/0.68 (define @t213 () (@quantifiers_skolemize @t206 1)) % 0.39/0.68 (define @t214 () (forall @t43 (or @t174 (_ @t213 @t24)))) % 0.39/0.68 (define @t215 () (not @t214)) % 0.39/0.68 (define @t216 () (forall @t46 (= (_ @t213 @t44) (_ @t210 (tptp.sub @t44 @t209))))) % 0.39/0.68 (define @t217 () (not @t216)) % 0.39/0.68 (define @t218 () (or @t217 @t215 @t212 @t211)) % 0.39/0.68 (define @t219 () (@list true)) % 0.39/0.68 (define @t220 () (@list @t218)) % 0.39/0.68 (define @t221 () (@list @t207)) % 0.39/0.68 (define @t222 () (_ @t213 @t207)) % 0.39/0.68 (define @t223 () (= @t222 @t211)) % 0.39/0.68 (define @t224 () (= @t211 @t222)) % 0.39/0.68 (define @t225 () (not @t222)) % 0.39/0.68 (define @t226 () (or @t212 @t222)) % 0.39/0.68 (assume @p1 (and (forall (@list @t158) (exists @t157 (= @t158 (_ tptp.d2term @t156)))) (forall @t157 (= @t156 tptp.d_one)) (forall (@list @t155 @t154) (=> (= (_ tptp.d2term @t155) (_ tptp.d2term @t154)) (= @t155 @t154))) (forall (@list @t153) (exists @t152 (= @t153 (_ tptp.d2subst @t151)))) (forall @t152 (= @t151 tptp.d_id)) (forall (@list @t150 @t149) (=> (= (_ tptp.d2subst @t150) (_ tptp.d2subst @t149)) (= @t150 @t149))) (= 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)) (= tptp.hoasinduction_p_and_p_prime (lambda (@list @t2 @t38) @t47)) @t148 (not (_ tptp.var @t85)) (= tptp.pushprop_lem1v2 @t130) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t28 (or (not (= (_ @t14 tptp.sh) (_ @t95 tptp.sh))) @t109))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t101) (= tptp.hoasinduction_lem3v2_f @t103) tptp.axvarshift (= tptp.hoasapinj2 @t123) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t119) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t81 (=> @t77 (=> @t91 (=> @t128 @t101))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t103) (= tptp.hoasinduction_lthm (=> @t62 (=> @t133 (=> @t105 @t36)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t64 (=> @t62 (=> @t50 (=> @t49 @t87))))) (= tptp.hoaslaminj @t114) (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t134) (or (not (forall (@list @t4 @t141) (or @t12 @t7 (not (forall (@list @t144 @t145 @t143) (= (_ (_ tptp.sub (_ (_ @t4 @t144) @t145)) @t143) (_ (_ tptp.sub (_ @t142 (_ (_ tptp.push @t145) @t144))) @t143)))) (not (forall (@list @t137 @t139 @t136) (= (_ (_ @t4 @t138) @t140) (_ @t142 (_ (_ tptp.push @t140) @t138)))))))) (not (forall @t43 (or @t27 (_ (_ @t3 (_ @t135 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t135 @t94))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t108) (= tptp.hoasinduction_lem3 @t105) (= tptp.hoasinduction_lem2 @t133) (= tptp.termmset_lthm (=> @t50 @t50)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t81 @t130)) tptp.hoasapnotvar (= tptp.hoasinduction_lem0 @t64) (= tptp.hoasinduction @t36) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t96) tptp.ulamvarind (= tptp.induction @t128) (= tptp.hoasinduction_lem3a_lthm (=> @t50 (=> @t108 @t89))) 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 @t48 (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 @t49) (= tptp.hoasapinj1_lthm (=> @t50 (=> @t121 @t119))) (= tptp.hoaslaminj_lthm (=> @t81 (=> @t77 (=> @t110 @t114)))) (= 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 @t110) (= tptp.hoasinduction_lem3_lthm (=> @t50 (=> @t108 @t105))) (= tptp.pushprop_lem0 @t74) tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t103 (=> @t50 @t49))) 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 (=> @t50 (=> @t101 @t62))) (= tptp.hoasinduction_lem0_lthm @t64) (= 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 @t62) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t81 (=> @t77 @t79))) (= tptp.hoasinduction_lem3v2 @t66) (= tptp.axshiftcons @t77) (= tptp.termmset @t50) (= tptp.pushprop_lem0_lthm @t74) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t50 @t66)) (= tptp.axvarid @t50) (= tptp.hoasinduction_lthm_3 (=> @t64 (=> @t62 (=> @t50 (=> @t49 @t36))))))) % 0.39/0.68 (assume @p2 @t167) % 0.39/0.68 (assume @p3 true) % 0.39/0.68 (step @p4 :rule refl :args (@t170)) % 0.39/0.68 (step @p5 :rule refl :args (@t171)) % 0.39/0.68 (step @p6 :rule refl :args (@t176)) % 0.39/0.68 (step @p7 :rule beta-reduce :args ((= @t181 @t180))) % 0.39/0.68 (step @p8 :rule cong :premises (@p7) :args (@t182)) % 0.39/0.68 (step @p9 :rule nary_cong :premises (@p8 @p6 @p5 @p4) :args (@t183)) % 0.39/0.68 (step @p10 :rule cong :premises (@p9) :args (@t185)) % 0.39/0.68 (step @p11 :rule bool-eq-true :args (@t185)) % 0.39/0.68 (step @p12 :rule eq-symm :args (true @t185)) % 0.39/0.68 (step @p13 :rule trans :premises (@p12 @p11)) % 0.39/0.68 (step @p14 :rule trans :premises (@p13 @p10)) % 0.39/0.68 (step @p15 :rule cong :premises (@p14) :args ((not (= true @t185)))) % 0.39/0.68 (step @p16 :rule refl :args (@t38)) % 0.39/0.68 (step @p17 :rule refl :args (@t52)) % 0.39/0.68 (step @p18 :rule refl :args (@t16)) % 0.39/0.68 (step @p19 :rule refl :args (@t8)) % 0.39/0.68 (step @p20 :rule refl :args ((_ @t52 @t69))) % 0.39/0.68 (step @p21 :rule refl :args ((tptp.sub @t44 @t67))) % 0.39/0.68 (step @p22 :rule refl :args (@t168)) % 0.39/0.68 (step @p23 :rule refl :args (@t44)) % 0.39/0.68 (step @p24 :rule cong :premises (@p23 @p22) :args (@t177)) % 0.39/0.68 (step @p25 :rule trans :premises (@p24 @p21)) % 0.39/0.68 (step @p26 :rule cong :premises (@p25) :args (@t178)) % 0.39/0.68 (step @p27 :rule trans :premises (@p26 @p20)) % 0.39/0.68 (step @p28 :rule refl :args (@t52)) % 0.39/0.68 (step @p29 :rule ho_cong :premises (@p28 @p25)) % 0.39/0.68 (step @p30 :rule cong :premises (@p29 @p27) :args ((= (_ @t52 @t177) @t178))) % 0.39/0.68 (step @p31 :rule symm :premises (@p30)) % 0.39/0.68 (step @p32 :rule refl :args (@t70)) % 0.39/0.68 (step @p33 :rule eq_resolve :premises (@p32 @p31)) % 0.39/0.68 (step @p34 :rule refl :args (@t68)) % 0.39/0.68 (step @p35 :rule ho_cong :premises (@p34 @p22)) % 0.39/0.68 (step @p36 :rule cong :premises (@p35 @p25) :args ((= (_ @t68 @t168) @t177))) % 0.39/0.68 (step @p37 :rule symm :premises (@p36)) % 0.39/0.68 (step @p38 :rule refl :args (@t69)) % 0.39/0.68 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 0.39/0.68 (step @p40 :rule refl :args (@t67)) % 0.39/0.68 (step @p41 :rule cong :premises (@p40 @p22) :args ((= @t67 @t168))) % 0.39/0.68 (step @p42 :rule symm :premises (@p41)) % 0.39/0.68 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.39/0.68 (step @p44 :rule ho_cong :premises (@p34 @p43)) % 0.39/0.68 (step @p45 :rule trans :premises (@p44 @p39)) % 0.39/0.68 (step @p46 :rule ho_cong :premises (@p28 @p45)) % 0.39/0.68 (step @p47 :rule trans :premises (@p46 @p33)) % 0.39/0.68 (step @p48 :rule refl :args (@t179)) % 0.39/0.68 (step @p49 :rule refl :args (@t45)) % 0.39/0.68 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t45 @t179))) % 0.39/0.68 (step @p51 :rule symm :premises (@p50)) % 0.39/0.68 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.39/0.68 (step @p53 :rule cong :premises (@p52 @p47) :args (@t71)) % 0.39/0.68 (step @p54 :rule cong :premises (@p53) :args (@t72)) % 0.39/0.68 (step @p55 :rule cong :premises (@p54) :args (@t147)) % 0.39/0.68 (step @p56 :rule refl :args (tptp.pushprop_p_and_p_prime)) % 0.39/0.68 (step @p57 :rule cong :premises (@p56 @p55) :args (@t148)) % 0.39/0.68 (step @p58 :rule and_elim :premises (@p1) :args (17)) % 0.39/0.68 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.39/0.68 (step @p60 :rule ho_cong :premises (@p59 @p19 @p18 @p17 @p16)) % 0.39/0.68 (step @p61 :rule cong :premises (@p60) :args (@t187)) % 0.39/0.68 (step @p62 :rule nary_cong :premises (@p61 @p6 @p5 @p4) :args (@t188)) % 0.39/0.68 (step @p63 :rule cong :premises (@p62) :args (@t189)) % 0.39/0.68 (step @p64 :rule bool-eq-true :args (tptp.pushprop_lem3v2)) % 0.39/0.68 (step @p65 :rule symm :premises (@p64)) % 0.39/0.68 (step @p66 :rule and_elim :premises (@p1) :args (117)) % 0.39/0.68 (step @p67 :rule eq_resolve :premises (@p66 @p65)) % 0.39/0.68 (step @p68 :rule cong :premises (@p67 @p63) :args (@t190)) % 0.39/0.68 (step @p69 :rule cong :premises (@p68) :args ((not @t190))) % 0.39/0.68 (step @p70 :rule trans :premises (@p69 @p15)) % 0.39/0.68 (step @p71 :rule aci_norm :args ((= @t192 @t188))) % 0.39/0.68 (step @p72 :rule cong :premises (@p71) :args (@t193)) % 0.39/0.68 (step @p73 :rule quant-merge-prenex :args ((= (forall @t129 @t195) @t193))) % 0.39/0.68 (step @p74 :rule alpha_equiv :args (@t196 (@list @t169) (@list @t24))) % 0.39/0.68 (step @p75 :rule refl :args (@t176)) % 0.39/0.68 (step @p76 :rule refl :args (@t187)) % 0.39/0.68 (step @p77 :rule nary_cong :premises (@p76 @p75 @p74) :args (@t197)) % 0.39/0.68 (step @p78 :rule quant-miniscope-or :args ((= @t195 @t197))) % 0.39/0.68 (step @p79 :rule trans :premises (@p78 @p77)) % 0.39/0.68 (step @p80 :rule symm :premises (@p79)) % 0.39/0.68 (step @p81 :rule cong :premises (@p80) :args ((forall @t129 (or @t187 @t176 @t200)))) % 0.39/0.68 (step @p82 :rule trans :premises (@p81 @p73)) % 0.39/0.68 (step @p83 :rule trans :premises (@p82 @p72)) % 0.39/0.68 (step @p84 :rule refl :args (@t200)) % 0.39/0.68 (step @p85 :rule refl :args (@t186)) % 0.39/0.68 (step @p86 :rule refl :args (@t163)) % 0.39/0.68 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t163 @t186))) % 0.39/0.68 (step @p88 :rule symm :premises (@p87)) % 0.39/0.68 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.39/0.68 (step @p90 :rule cong :premises (@p89) :args (@t201)) % 0.39/0.68 (step @p91 :rule nary_cong :premises (@p90 @p75 @p84) :args (@t202)) % 0.39/0.68 (step @p92 :rule cong :premises (@p91) :args ((forall @t129 @t202))) % 0.39/0.68 (step @p93 :rule trans :premises (@p92 @p83)) % 0.39/0.68 (step @p94 :rule aci_norm :args ((= (or @t201 (or @t176 @t200)) @t202))) % 0.39/0.68 (step @p95 :rule bool-impl-elim :args (@t175 @t200)) % 0.39/0.68 (step @p96 :rule refl :args (@t201)) % 0.39/0.68 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t201 @t203))) % 0.39/0.68 (step @p98 :rule trans :premises (@p97 @p94)) % 0.39/0.68 (step @p99 :rule bool-impl-elim :args (@t163 @t203)) % 0.39/0.68 (step @p100 :rule trans :premises (@p99 @p98)) % 0.39/0.68 (step @p101 :rule cong :premises (@p100) :args ((forall @t129 (=> @t163 @t203)))) % 0.39/0.68 (step @p102 :rule trans :premises (@p101 @p93)) % 0.39/0.68 (step @p103 :rule refl :args ((_ @t52 @t102))) % 0.39/0.68 (step @p104 :rule refl :args ((tptp.sub @t24 @t67))) % 0.39/0.68 (step @p105 :rule refl :args (@t24)) % 0.39/0.68 (step @p106 :rule cong :premises (@p105 @p22) :args (@t198)) % 0.39/0.68 (step @p107 :rule trans :premises (@p106 @p104)) % 0.39/0.68 (step @p108 :rule cong :premises (@p107) :args (@t199)) % 0.39/0.68 (step @p109 :rule trans :premises (@p108 @p103)) % 0.39/0.68 (step @p110 :rule ho_cong :premises (@p28 @p107)) % 0.39/0.68 (step @p111 :rule cong :premises (@p110 @p109) :args ((= (_ @t52 @t198) @t199))) % 0.39/0.68 (step @p112 :rule symm :premises (@p111)) % 0.39/0.68 (step @p113 :rule refl :args (@t159)) % 0.39/0.68 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.39/0.68 (step @p115 :rule refl :args (@t95)) % 0.39/0.68 (step @p116 :rule ho_cong :premises (@p115 @p22)) % 0.39/0.68 (step @p117 :rule cong :premises (@p116 @p107) :args ((= (_ @t95 @t168) @t198))) % 0.39/0.68 (step @p118 :rule symm :premises (@p117)) % 0.39/0.68 (step @p119 :rule refl :args (@t102)) % 0.39/0.68 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.39/0.68 (step @p121 :rule ho_cong :premises (@p115 @p43)) % 0.39/0.68 (step @p122 :rule trans :premises (@p121 @p120)) % 0.39/0.68 (step @p123 :rule ho_cong :premises (@p28 @p122)) % 0.39/0.68 (step @p124 :rule trans :premises (@p123 @p114)) % 0.39/0.68 (step @p125 :rule refl :args (@t173)) % 0.39/0.68 (step @p126 :rule refl :args (@t99)) % 0.39/0.68 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t99 @t173))) % 0.39/0.68 (step @p128 :rule symm :premises (@p127)) % 0.39/0.68 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.39/0.68 (step @p130 :rule cong :premises (@p129) :args (@t100)) % 0.39/0.68 (step @p131 :rule nary_cong :premises (@p130 @p124) :args (@t204)) % 0.39/0.68 (step @p132 :rule cong :premises (@p131) :args ((forall @t43 @t204))) % 0.39/0.68 (step @p133 :rule bool-impl-elim :args (@t99 @t159)) % 0.39/0.68 (step @p134 :rule cong :premises (@p133) :args (@t160)) % 0.39/0.68 (step @p135 :rule trans :premises (@p134 @p132)) % 0.39/0.68 (step @p136 :rule refl :args (@t172)) % 0.39/0.68 (step @p137 :rule refl :args (@t41)) % 0.39/0.68 (step @p138 :rule cong :premises (@p137 @p136) :args ((= @t41 @t172))) % 0.39/0.68 (step @p139 :rule symm :premises (@p138)) % 0.39/0.68 (step @p140 :rule eq_resolve :premises (@p137 @p139)) % 0.39/0.68 (step @p141 :rule nary_cong :premises (@p130 @p140) :args (@t205)) % 0.39/0.68 (step @p142 :rule cong :premises (@p141) :args ((forall @t43 @t205))) % 0.39/0.68 (step @p143 :rule bool-impl-elim :args (@t99 @t41)) % 0.39/0.68 (step @p144 :rule cong :premises (@p143) :args (@t161)) % 0.39/0.68 (step @p145 :rule trans :premises (@p144 @p142)) % 0.39/0.68 (step @p146 :rule cong :premises (@p145 @p135) :args (@t162)) % 0.39/0.68 (step @p147 :rule refl :args (@t163)) % 0.39/0.68 (step @p148 :rule cong :premises (@p147 @p146) :args (@t164)) % 0.39/0.68 (step @p149 :rule cong :premises (@p148) :args (@t165)) % 0.39/0.68 (step @p150 :rule trans :premises (@p149 @p102)) % 0.39/0.68 (step @p151 :rule refl :args (tptp.pushprop_lem3v2)) % 0.39/0.68 (step @p152 :rule cong :premises (@p151 @p150) :args (@t166)) % 0.39/0.68 (step @p153 :rule cong :premises (@p152) :args (@t167)) % 0.39/0.68 (step @p154 :rule trans :premises (@p153 @p70)) % 0.39/0.68 (step @p155 :rule eq_resolve :premises (@p2 @p154)) % 0.39/0.68 (step @p156 :rule skolemize :premises (@p155)) % 0.39/0.68 (step @p157 :rule bool-double-not-elim :args (@t208)) % 0.39/0.68 (step @p158 :rule refl :args (@t218)) % 0.39/0.68 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((or @t218 (not @t212)))) % 0.39/0.68 (step @p160 :rule cnf_or_neg :args (@t218 2)) % 0.39/0.68 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.39/0.68 (step @p162 :rule reordering :premises (@p161) :args ((or @t208 @t218))) % 0.39/0.68 (step @p163 :rule chain_m_resolution :premises (@p162 @p156) :args (@t208 @t219 @t220)) % 0.39/0.68 (step @p164 :rule bool-double-not-elim :args (@t214)) % 0.39/0.68 (step @p165 :rule nary_cong :premises (@p158 @p164) :args ((or @t218 (not @t215)))) % 0.39/0.68 (step @p166 :rule cnf_or_neg :args (@t218 1)) % 0.39/0.68 (step @p167 :rule eq_resolve :premises (@p166 @p165)) % 0.39/0.68 (step @p168 :rule reordering :premises (@p167) :args ((or @t214 @t218))) % 0.39/0.68 (step @p169 :rule chain_m_resolution :premises (@p168 @p156) :args (@t214 @t219 @t220)) % 0.39/0.68 (step @p170 :rule instantiate :premises (@p169) :args (@t221)) % 0.39/0.68 (step @p171 :rule bool-double-not-elim :args (@t216)) % 0.39/0.68 (step @p172 :rule nary_cong :premises (@p158 @p171) :args ((or @t218 (not @t217)))) % 0.39/0.68 (step @p173 :rule cnf_or_neg :args (@t218 0)) % 0.39/0.68 (step @p174 :rule eq_resolve :premises (@p173 @p172)) % 0.39/0.68 (step @p175 :rule reordering :premises (@p174) :args ((or @t216 @t218))) % 0.39/0.68 (step @p176 :rule chain_m_resolution :premises (@p175 @p156) :args (@t216 @t219 @t220)) % 0.39/0.68 (step @p177 :rule eq-symm :args (@t222 @t211)) % 0.39/0.68 (step @p178 :rule refl :args (@t216)) % 0.39/0.68 (step @p179 :rule cong :premises (@p178 @p177) :args ((=> @t216 @t223))) % 0.39/0.68 (assume-push @p195 @t216) % 0.39/0.68 (step @p181 :rule instantiate :premises (@p176) :args (@t221)) % 0.39/0.68 (step-pop @p196 :rule scope :premises (@p181)) % 0.39/0.68 (step @p182 :rule process_scope :premises (@p196) :args (@t223)) % 0.39/0.68 (step @p184 :rule eq_resolve :premises (@p182 @p179)) % 0.39/0.68 (step @p185 :rule implies_elim :premises (@p184)) % 0.39/0.68 (step @p186 :rule chain_m_resolution :premises (@p185 @p176) :args (@t224 (@list false) (@list @t216))) % 0.39/0.68 (step @p187 :rule cnf_or_neg :args (@t218 3)) % 0.39/0.68 (step @p188 :rule chain_m_resolution :premises (@p187 @p156) :args ((not @t211) @t219 @t220)) % 0.39/0.68 (step @p189 :rule cnf_equiv_pos2 :args (@t224)) % 0.39/0.68 (step @p190 :rule reordering :premises (@p189) :args ((or @t211 @t225 (not @t224)))) % 0.39/0.68 (step @p191 :rule chain_m_resolution :premises (@p190 @p188 @p186) :args (@t225 (@list true false) (@list @t211 @t224))) % 0.39/0.68 (step @p192 :rule cnf_or_pos :args (@t226)) % 0.39/0.68 (step @p193 :rule reordering :premises (@p192) :args ((or @t212 @t222 (not @t226)))) % 0.39/0.68 (step @p194 false :rule chain_m_resolution :premises (@p193 @p191 @p170 @p163) :args (false (@list true false false) (@list @t222 @t226 @t208))) % 0.39/0.68 ) % 0.39/0.68 % SZS output end Proof % 0.39/0.68 % cvc5 exiting %------------------------------------------------------------------------------