%------------------------------------------------------------------------------ % 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 : n019.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 175.23s 175.52s % Output : Proof 175.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % 0.08/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n019.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 23:02:34 EDT 2026 % 0.19/0.35 % CPUTime : % 0.39/0.57 %----Proving TH0 % 175.23/175.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 175.23/175.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 175.23/175.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 175.23/175.52 --- Run --ho-elim --full-saturate-quant at 18s... % 175.23/175.52 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 175.23/175.52 % SZS status Theorem % 175.23/175.52 % SZS output start Proof % 175.23/175.52 ( % 175.23/175.52 (declare-sort tptp.subst 0) % 175.23/175.52 (declare-sort tptp.term 0) % 175.23/175.52 (declare-sort tptp.d_term 0) % 175.23/175.52 (declare-sort tptp.d_subst 0) % 175.23/175.52 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 175.23/175.52 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 175.23/175.52 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 175.23/175.52 (declare-const tptp.pushprop_lem1v2 Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem1_gthm Bool) % 175.23/175.52 (declare-const tptp.axmap Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem0_gthm Bool) % 175.23/175.52 (declare-const tptp.shinj Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem1v2 Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 175.23/175.52 (declare-const tptp.induction2lem Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 175.23/175.52 (declare-const tptp.axvarshift Bool) % 175.23/175.52 (declare-const tptp.hoasapinj2 Bool) % 175.23/175.52 (declare-const tptp.hoasapnotvar_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasapinj1 Bool) % 175.23/175.52 (declare-const tptp.ulamvar1 Bool) % 175.23/175.52 (declare-const tptp.induction2lem_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 175.23/175.52 (declare-const tptp.apnotvar Bool) % 175.23/175.52 (declare-const tptp.pushprop_lthm_orig Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 175.23/175.52 (declare-const tptp.hoaslaminj Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3aaa Bool) % 175.23/175.52 (declare-const tptp.induction2lem_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3 Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem2 Bool) % 175.23/175.52 (declare-const tptp.termmset_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem1 Bool) % 175.23/175.52 (declare-const tptp.hoaslamnotap_lthm Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasapnotvar Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem0 Bool) % 175.23/175.52 (declare-const tptp.hoasinduction Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_gthm Bool) % 175.23/175.52 (declare-const tptp.axapp Bool) % 175.23/175.52 (declare-const tptp.hoaslamnotvar_lthm Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 175.23/175.52 (declare-const tptp.ulamvarind Bool) % 175.23/175.52 (declare-const tptp.induction Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 175.23/175.52 (declare-const tptp.termmset_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3aa Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 175.23/175.52 (declare-const tptp.hoaslamnotap_gthm Bool) % 175.23/175.52 (declare-const tptp.hoaslamnotvar_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem2v2 Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 175.23/175.52 (declare-const tptp.axclos Bool) % 175.23/175.52 (declare-const tptp.axassoc Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem2v2 Bool) % 175.23/175.52 (declare-const tptp.pushprop_lthm Bool) % 175.23/175.52 (declare-const tptp.apinj2 Bool) % 175.23/175.52 (declare-const tptp.apinj1 Bool) % 175.23/175.52 (declare-const tptp.hoasapinj2_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3v2a Bool) % 175.23/175.52 (declare-const tptp.hoasapinj1_lthm Bool) % 175.23/175.52 (declare-const tptp.hoaslaminj_lthm Bool) % 175.23/175.52 (declare-const tptp.axvarcons Bool) % 175.23/175.52 (declare-const tptp.axscons Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 175.23/175.52 (declare-const tptp.d_one tptp.d_term) % 175.23/175.52 (declare-const tptp.hoaslamnotap Bool) % 175.23/175.52 (declare-const tptp.ulamvarsh Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem3v2 Bool) % 175.23/175.52 (declare-const tptp.axshiftcons Bool) % 175.23/175.52 (declare-const tptp.id tptp.subst) % 175.23/175.52 (declare-const tptp.pushprop_lem1_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 175.23/175.52 (declare-const tptp.pushprop_lem0_lthm Bool) % 175.23/175.52 (declare-const tptp.one tptp.term) % 175.23/175.52 (declare-const tptp.substmonoid_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3v2 Bool) % 175.23/175.52 (declare-const tptp.sh tptp.subst) % 175.23/175.52 (declare-const tptp.termmset Bool) % 175.23/175.52 (declare-const tptp.induction2 Bool) % 175.23/175.52 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 175.23/175.52 (declare-const tptp.lam (-> tptp.term tptp.term)) % 175.23/175.52 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 175.23/175.52 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 175.23/175.52 (declare-const tptp.axvarid Bool) % 175.23/175.52 (declare-const tptp.d_id tptp.d_subst) % 175.23/175.52 (declare-const tptp.var (-> tptp.term Bool)) % 175.23/175.52 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 175.23/175.52 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 175.23/175.52 (declare-const tptp.hoasapnotvar_lthm Bool) % 175.23/175.52 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 175.23/175.52 (declare-const tptp.hoasinduction_lthm_3 Bool) % 175.23/175.52 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 175.23/175.52 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 175.23/175.52 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 175.23/175.52 (declare-const tptp.induction2_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3a Bool) % 175.23/175.52 (declare-const tptp.lamnotvar Bool) % 175.23/175.52 (declare-const tptp.substmonoid Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3b Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 175.23/175.52 (declare-const tptp.pushprop Bool) % 175.23/175.52 (declare-const tptp.substmonoid_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 175.23/175.52 (declare-const tptp.induction2_lthm Bool) % 175.23/175.52 (declare-const tptp.hoaslaminj_gthm Bool) % 175.23/175.52 (declare-const tptp.axidl Bool) % 175.23/175.52 (declare-const tptp.hoaslamnotvar Bool) % 175.23/175.52 (declare-const tptp.hoasapinj1_gthm Bool) % 175.23/175.52 (declare-const tptp.lamnotap Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasapinj2_gthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 175.23/175.52 (declare-const tptp.axabs Bool) % 175.23/175.52 (declare-const tptp.pushprop_gthm Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem0 Bool) % 175.23/175.52 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 175.23/175.52 (declare-const tptp.laminj Bool) % 175.23/175.52 (declare-const tptp.pushprop_lem1 Bool) % 175.23/175.52 (declare-const tptp.axidr Bool) % 175.23/175.52 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 175.23/175.52 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 175.23/175.52 (define @t3 () (_ @t2 tptp.id)) % 175.23/175.52 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 175.23/175.52 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 175.23/175.52 (define @t6 () (_ tptp.lam @t5)) % 175.23/175.52 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 175.23/175.52 (define @t8 () (@var "A" tptp.term)) % 175.23/175.52 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 175.23/175.52 (define @t10 () (not @t9)) % 175.23/175.52 (define @t11 () (@list @t8)) % 175.23/175.52 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 175.23/175.52 (define @t13 () (@var "N" tptp.subst)) % 175.23/175.52 (define @t14 () (_ tptp.sub @t8)) % 175.23/175.52 (define @t15 () (_ @t14 @t13)) % 175.23/175.52 (define @t16 () (@var "M" tptp.subst)) % 175.23/175.52 (define @t17 () (_ tptp.comp @t16)) % 175.23/175.52 (define @t18 () (_ @t17 @t13)) % 175.23/175.52 (define @t19 () (_ (_ @t4 @t18) @t15)) % 175.23/175.52 (define @t20 () (_ (_ @t4 @t16) @t8)) % 175.23/175.52 (define @t21 () (_ (_ tptp.sub @t20) @t13)) % 175.23/175.52 (define @t22 () (= @t21 @t19)) % 175.23/175.52 (define @t23 () (@list @t16 @t8 @t13)) % 175.23/175.52 (define @t24 () (forall @t23 @t22)) % 175.23/175.52 (define @t25 () (not @t24)) % 175.23/175.52 (define @t26 () (@list @t4)) % 175.23/175.52 (define @t27 () (not (forall @t26 (or @t25 @t12 @t7)))) % 175.23/175.52 (define @t28 () (@var "B" tptp.term)) % 175.23/175.52 (define @t29 () (_ @t14 tptp.id)) % 175.23/175.52 (define @t30 () (_ tptp.ap @t29)) % 175.23/175.52 (define @t31 () (not (_ (_ @t3 @t28) tptp.id))) % 175.23/175.52 (define @t32 () (@list @t8 @t28)) % 175.23/175.52 (define @t33 () (not (forall @t32 (or @t10 @t31 (_ (_ @t3 (_ @t30 @t28)) tptp.id))))) % 175.23/175.52 (define @t34 () (@var "K" tptp.subst)) % 175.23/175.52 (define @t35 () (_ (_ (_ @t2 @t16) @t8) (_ (_ tptp.comp @t34) @t13))) % 175.23/175.52 (define @t36 () (_ (_ (_ @t2 (_ @t17 @t34)) (_ @t14 @t34)) @t13)) % 175.23/175.52 (define @t37 () (@list @t16 @t8 @t13 @t34)) % 175.23/175.52 (define @t38 () (not (forall @t37 (or (not @t36) @t35)))) % 175.23/175.52 (define @t39 () (not (forall @t37 (or (not @t35) @t36)))) % 175.23/175.52 (define @t40 () (forall (@list @t2 @t1) (or @t39 @t38 (not (forall @t11 (or (not (_ tptp.var @t29)) @t9))) @t33 @t27 (_ (_ @t3 @t1) tptp.id)))) % 175.23/175.52 (define @t41 () (@var "Bound_variable_2931" tptp.term)) % 175.23/175.52 (define @t42 () (@var "Q" (-> tptp.term Bool))) % 175.23/175.52 (define @t43 () (_ tptp.push @t28)) % 175.23/175.52 (define @t44 () (_ @t43 tptp.id)) % 175.23/175.52 (define @t45 () (not (_ @t42 @t28))) % 175.23/175.52 (define @t46 () (@list @t28)) % 175.23/175.52 (define @t47 () (@var "X" tptp.term)) % 175.23/175.52 (define @t48 () (_ @t42 @t47)) % 175.23/175.52 (define @t49 () (@list @t47)) % 175.23/175.52 (define @t50 () (forall @t49 (= @t48 (_ (_ @t3 @t47) tptp.id)))) % 175.23/175.52 (define @t51 () (not @t50)) % 175.23/175.52 (define @t52 () (forall (@list @t2 @t42 @t41) (or @t27 @t51 (not (forall @t46 (or @t45 (_ @t42 (_ (_ tptp.sub @t41) @t44))))) (_ @t42 (_ tptp.lam @t41))))) % 175.23/175.52 (define @t53 () (forall @t11 (= @t8 @t29))) % 175.23/175.52 (define @t54 () (@var "Bound_variable_2367" tptp.term)) % 175.23/175.52 (define @t55 () (@var "P" (-> tptp.term Bool))) % 175.23/175.52 (define @t56 () (_ tptp.lam @t8)) % 175.23/175.52 (define @t57 () (_ @t55 @t56)) % 175.23/175.52 (define @t58 () (not (_ @t55 @t28))) % 175.23/175.52 (define @t59 () (not (forall @t11 (or (not (forall @t46 (or @t58 (_ @t55 (_ @t14 @t44))))) @t57)))) % 175.23/175.52 (define @t60 () (_ tptp.ap @t8)) % 175.23/175.52 (define @t61 () (_ @t55 @t8)) % 175.23/175.52 (define @t62 () (not @t61)) % 175.23/175.52 (define @t63 () (not (forall @t32 (or @t62 @t58 (_ @t55 (_ @t60 @t28)))))) % 175.23/175.52 (define @t64 () (not (forall @t11 (or (not (_ tptp.var @t8)) @t61)))) % 175.23/175.52 (define @t65 () (forall (@list @t55 @t54) (or @t64 @t63 @t59 (_ @t55 @t54)))) % 175.23/175.52 (define @t66 () (@list @t42)) % 175.23/175.52 (define @t67 () (forall (@list @t2) (not (forall @t66 @t51)))) % 175.23/175.52 (define @t68 () (@var "Bound_variable_2910" tptp.term)) % 175.23/175.52 (define @t69 () (forall (@list @t2 @t42 @t68) (or @t39 @t38 @t27 @t51 (not (forall @t46 (or @t45 (_ @t42 (_ (_ tptp.sub @t68) @t44))))) (_ @t42 (_ tptp.lam @t68))))) % 175.23/175.52 (define @t70 () (_ (_ tptp.push @t8) @t16)) % 175.23/175.52 (define @t71 () (forall @t49 (= @t48 (_ @t55 (_ (_ tptp.sub @t47) @t70))))) % 175.23/175.52 (define @t72 () (not @t71)) % 175.23/175.52 (define @t73 () (forall (@list @t55 @t8 @t16) (not (forall @t66 @t72)))) % 175.23/175.52 (define @t74 () (_ tptp.comp tptp.sh)) % 175.23/175.52 (define @t75 () (@list @t8 @t16)) % 175.23/175.52 (define @t76 () (forall @t75 (= @t16 (_ @t74 @t70)))) % 175.23/175.52 (define @t77 () (@var "K" (-> tptp.term Bool))) % 175.23/175.52 (define @t78 () (forall (@list @t55 @t77 @t8 @t16 @t28) (or @t62 (_ @t77 (_ @t14 (_ @t43 @t16)))))) % 175.23/175.52 (define @t79 () (_ tptp.sub tptp.one)) % 175.23/175.52 (define @t80 () (forall @t75 (= @t8 (_ @t79 @t70)))) % 175.23/175.52 (define @t81 () (@var "Bound_variable_2605" tptp.term)) % 175.23/175.52 (define @t82 () (@var "Bound_variable_2603" tptp.term)) % 175.23/175.52 (define @t83 () (_ tptp.d2subst tptp.d_id)) % 175.23/175.52 (define @t84 () (_ tptp.d2term tptp.d_one)) % 175.23/175.52 (define @t85 () (@var "Bound_variable_3295" tptp.term)) % 175.23/175.52 (define @t86 () (forall (@list @t2 @t85) (or @t33 @t27 (_ (_ @t3 @t85) tptp.id)))) % 175.23/175.52 (define @t87 () (@var "Bound_variable_3232" tptp.term)) % 175.23/175.52 (define @t88 () (forall (@list @t2 @t87) (or @t27 (not (forall @t46 (or @t31 (_ (_ @t3 (_ (_ tptp.sub @t87) @t44)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t87)) tptp.id)))) % 175.23/175.52 (define @t89 () (@list @t16)) % 175.23/175.52 (define @t90 () (forall @t89 (= @t16 (_ @t17 tptp.id)))) % 175.23/175.52 (define @t91 () (forall @t89 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 175.23/175.52 (define @t92 () (and @t91 @t90)) % 175.23/175.52 (define @t93 () (_ (_ tptp.push tptp.one) tptp.sh)) % 175.23/175.52 (define @t94 () (_ tptp.sub @t28)) % 175.23/175.52 (define @t95 () (forall @t46 (not (forall @t26 (not (= @t5 (_ @t94 @t93))))))) % 175.23/175.52 (define @t96 () (@var "Bound_variable_2342" tptp.subst)) % 175.23/175.52 (define @t97 () (@var "Bound_variable_2340" tptp.term)) % 175.23/175.52 (define @t98 () (forall (@list @t55 @t97 @t96) (or @t63 @t59 (not (forall @t46 (or (not (_ tptp.var @t28)) (_ @t55 (_ @t94 @t96))))) (_ @t55 (_ (_ tptp.sub @t97) @t96))))) % 175.23/175.52 (define @t99 () (forall @t46 (not (forall @t26 (not (forall @t75 (= (_ @t94 @t70) @t20))))))) % 175.23/175.52 (define @t100 () (@var "Bound_variable_3211" tptp.term)) % 175.23/175.52 (define @t101 () (forall (@list @t2 @t100) (or @t39 @t38 @t27 (not (forall @t46 (or @t31 (_ (_ @t3 (_ (_ tptp.sub @t100) @t44)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t100)) tptp.id)))) % 175.23/175.52 (define @t102 () (@var "Bound_variable_3046" tptp.term)) % 175.23/175.52 (define @t103 () (_ tptp.sub @t102)) % 175.23/175.52 (define @t104 () (forall (@list @t2 @t102) (or @t27 (not (forall @t46 (or @t31 (_ (_ @t3 (_ @t103 @t44)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t103 @t93))) tptp.id)))) % 175.23/175.52 (define @t105 () (= @t8 @t28)) % 175.23/175.52 (define @t106 () (forall @t32 (or (not (= @t56 (_ tptp.lam @t28))) @t105))) % 175.23/175.52 (define @t107 () (@var "Bound_variable_2551" tptp.term)) % 175.23/175.52 (define @t108 () (@var "Bound_variable_2549" tptp.subst)) % 175.23/175.52 (define @t109 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 175.23/175.52 (define @t110 () (_ (_ @t109 @t108) @t107)) % 175.23/175.52 (define @t111 () (_ (_ @t4 @t108) @t107)) % 175.23/175.52 (define @t112 () (= @t111 @t110)) % 175.23/175.52 (define @t113 () (_ (_ @t109 tptp.sh) tptp.one)) % 175.23/175.52 (define @t114 () (_ tptp.lam @t113)) % 175.23/175.52 (define @t115 () (= @t6 @t114)) % 175.23/175.52 (define @t116 () (not @t115)) % 175.23/175.52 (define @t117 () (_ (_ @t109 @t18) @t15)) % 175.23/175.52 (define @t118 () (_ (_ @t109 @t16) @t8)) % 175.23/175.52 (define @t119 () (_ (_ tptp.sub @t118) @t13)) % 175.23/175.52 (define @t120 () (= @t119 @t117)) % 175.23/175.52 (define @t121 () (forall @t23 @t120)) % 175.23/175.52 (define @t122 () (not @t121)) % 175.23/175.52 (define @t123 () (or @t25 @t122 @t116 @t112)) % 175.23/175.52 (define @t124 () (@list @t4 @t109 @t108 @t107)) % 175.23/175.52 (define @t125 () (forall @t124 @t123)) % 175.23/175.52 (define @t126 () (@var "D" tptp.term)) % 175.23/175.52 (define @t127 () (@var "C" tptp.term)) % 175.23/175.52 (define @t128 () (not (= (_ @t30 @t127) (_ (_ tptp.ap (_ @t94 tptp.id)) @t126)))) % 175.23/175.52 (define @t129 () (@list @t8 @t28 @t127 @t126)) % 175.23/175.52 (define @t130 () (forall @t129 (or @t128 @t105))) % 175.23/175.52 (define @t131 () (not (= (_ @t60 @t127) (_ (_ tptp.ap @t28) @t126)))) % 175.23/175.52 (define @t132 () (forall @t129 (or @t131 @t105))) % 175.23/175.52 (define @t133 () (= @t127 @t126)) % 175.23/175.52 (define @t134 () (forall @t129 (or @t128 @t133))) % 175.23/175.52 (define @t135 () (forall @t129 (or @t131 @t133))) % 175.23/175.52 (define @t136 () (@var "Bound_variable_2822" tptp.term)) % 175.23/175.52 (define @t137 () (@var "Bound_variable_2820" tptp.term)) % 175.23/175.52 (define @t138 () (@var "Bound_variable_2140" tptp.term)) % 175.23/175.52 (define @t139 () (forall (@list @t55 @t138) (or @t64 @t63 (not (forall @t11 (or @t62 @t57))) (_ @t55 @t138)))) % 175.23/175.52 (define @t140 () (forall (@list @t55 @t42 @t8 @t16) (or @t62 @t72 (_ @t42 tptp.one)))) % 175.23/175.52 (define @t141 () (@var "Bound_variable_3001" tptp.term)) % 175.23/175.52 (define @t142 () (@var "Bound_variable_2999" tptp.term)) % 175.23/175.52 (define @t143 () (forall (@list @t2 @t142 @t141) (or @t39 @t38 @t33 (not (_ (_ @t3 @t142) tptp.id)) (not (_ (_ @t3 @t141) tptp.id)) (_ (_ @t3 (_ (_ tptp.ap @t142) @t141)) tptp.id)))) % 175.23/175.52 (define @t144 () (@var "Bound_variable_3171" tptp.term)) % 175.23/175.52 (define @t145 () (_ tptp.sub @t144)) % 175.23/175.52 (define @t146 () (@var "Bound_variable_3094" tptp.subst)) % 175.23/175.52 (define @t147 () (@var "Bound_variable_3090" tptp.subst)) % 175.23/175.52 (define @t148 () (_ (_ tptp.comp @t147) @t146)) % 175.23/175.52 (define @t149 () (@var "Bound_variable_3092" tptp.term)) % 175.23/175.52 (define @t150 () (_ (_ tptp.sub @t149) @t146)) % 175.23/175.52 (define @t151 () (@var "Bound_variable_3149" tptp.term)) % 175.23/175.52 (define @t152 () (_ tptp.sub @t151)) % 175.23/175.52 (define @t153 () (@var "Bound_variable_3076" tptp.subst)) % 175.23/175.52 (define @t154 () (@var "Bound_variable_3072" tptp.subst)) % 175.23/175.52 (define @t155 () (@var "Bound_variable_3074" tptp.term)) % 175.23/175.52 (define @t156 () (= tptp.hoaslaminj @t125)) % 175.23/175.52 (define @t157 () (lambda (@list (@var "Bound_variable_4913" tptp.subst) (@var "Bound_variable_4915" (-> tptp.subst tptp.term tptp.term))) @t84)) % 175.23/175.52 (define @t158 () (_ (_ tptp.comp @t83) @t83)) % 175.23/175.52 (define @t159 () (_ (_ tptp.sub @t84) @t83)) % 175.23/175.52 (define @t160 () (@var "DS2" tptp.d_subst)) % 175.23/175.52 (define @t161 () (@var "DS1" tptp.d_subst)) % 175.23/175.52 (define @t162 () (@var "DS" tptp.d_subst)) % 175.23/175.52 (define @t163 () (@list @t162)) % 175.23/175.52 (define @t164 () (forall @t163 (= @t162 tptp.d_id))) % 175.23/175.52 (define @t165 () (_ tptp.d2subst @t162)) % 175.23/175.52 (define @t166 () (@var "S" tptp.subst)) % 175.23/175.52 (define @t167 () (= @t166 @t165)) % 175.23/175.52 (define @t168 () (exists @t163 @t167)) % 175.23/175.52 (define @t169 () (@list @t166)) % 175.23/175.52 (define @t170 () (forall @t169 @t168)) % 175.23/175.52 (define @t171 () (@var "DT2" tptp.d_term)) % 175.23/175.52 (define @t172 () (@var "DT1" tptp.d_term)) % 175.23/175.52 (define @t173 () (@var "DT" tptp.d_term)) % 175.23/175.52 (define @t174 () (@list @t173)) % 175.23/175.52 (define @t175 () (forall @t174 (= @t173 tptp.d_one))) % 175.23/175.52 (define @t176 () (_ tptp.d2term @t173)) % 175.23/175.52 (define @t177 () (@var "T" tptp.term)) % 175.23/175.52 (define @t178 () (= @t177 @t176)) % 175.23/175.52 (define @t179 () (exists @t174 @t178)) % 175.23/175.52 (define @t180 () (@list @t177)) % 175.23/175.52 (define @t181 () (forall @t180 @t179)) % 175.23/175.52 (define @t182 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 175.23/175.52 (define @t183 () (_ (_ @t182 @t16) @t8)) % 175.23/175.52 (define @t184 () (= @t20 @t183)) % 175.23/175.52 (define @t185 () (@list @t16 @t8)) % 175.23/175.52 (define @t186 () (forall @t185 @t184)) % 175.23/175.52 (define @t187 () (lambda @t185 @t183)) % 175.23/175.52 (define @t188 () (_ tptp.hoaslam tptp.id)) % 175.23/175.52 (define @t189 () (_ @t188 @t187)) % 175.23/175.52 (define @t190 () (lambda @t185 @t20)) % 175.23/175.52 (define @t191 () (_ @t188 @t190)) % 175.23/175.52 (define @t192 () (= @t191 @t189)) % 175.23/175.52 (define @t193 () (=> @t192 @t186)) % 175.23/175.52 (define @t194 () (_ (_ @t182 @t18) @t15)) % 175.23/175.52 (define @t195 () (_ (_ tptp.sub @t183) @t13)) % 175.23/175.52 (define @t196 () (= @t195 @t194)) % 175.23/175.52 (define @t197 () (forall @t23 @t196)) % 175.23/175.52 (define @t198 () (=> @t197 @t193)) % 175.23/175.52 (define @t199 () (@list @t182)) % 175.23/175.52 (define @t200 () (forall @t199 @t198)) % 175.23/175.52 (define @t201 () (=> @t24 @t200)) % 175.23/175.52 (define @t202 () (forall @t26 @t201)) % 175.23/175.52 (define @t203 () (= tptp.hoaslaminj @t202)) % 175.23/175.52 (define @t204 () (not @t203)) % 175.23/175.52 (define @t205 () (@const 0 (@ho-elim-sort (-> tptp.d_subst tptp.subst)))) % 175.23/175.52 (define @t206 () (@const 1 (-> (@ho-elim-sort (-> tptp.d_subst tptp.subst)) tptp.d_subst tptp.subst))) % 175.23/175.52 (define @t207 () (_ @t206 @t205 tptp.d_id)) % 175.23/175.52 (define @t208 () (@const 2 (@ho-elim-sort (-> tptp.d_term tptp.term)))) % 175.23/175.52 (define @t209 () (@const 3 (-> (@ho-elim-sort (-> tptp.d_term tptp.term)) tptp.d_term tptp.term))) % 175.23/175.52 (define @t210 () (_ @t209 @t208 tptp.d_one)) % 175.23/175.52 (define @t211 () (@const 4 (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)))) % 175.23/175.52 (define @t212 () (@const 5 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term))))) % 175.23/175.52 (define @t213 () (@const 6 (-> (@ho-elim-sort (-> tptp.subst tptp.term)) tptp.subst tptp.term))) % 175.23/175.52 (define @t214 () (_ @t213 (_ @t212 @t211 @t210) @t207)) % 175.23/175.52 (define @t215 () (= @t210 @t214)) % 175.23/175.52 (define @t216 () (@const 7 (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)))) % 175.23/175.52 (define @t217 () (@const 8 (-> (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)) tptp.subst (@ho-elim-sort (-> tptp.subst tptp.subst))))) % 175.23/175.52 (define @t218 () (@const 9 (-> (@ho-elim-sort (-> tptp.subst tptp.subst)) tptp.subst tptp.subst))) % 175.23/175.52 (define @t219 () (_ @t218 (_ @t217 @t216 @t207) @t207)) % 175.23/175.52 (define @t220 () (= @t207 @t219)) % 175.23/175.52 (define @t221 () (_ @t209 @t208 @t173)) % 175.23/175.52 (define @t222 () (forall @t180 (not (forall @t174 (not (= @t177 @t221)))))) % 175.23/175.52 (define @t223 () (tptp.d2term @t173)) % 175.23/175.52 (define @t224 () (not @t178)) % 175.23/175.52 (define @t225 () (forall @t174 @t224)) % 175.23/175.52 (define @t226 () (not @t225)) % 175.23/175.52 (define @t227 () (@var "z" tptp.term)) % 175.23/175.52 (define @t228 () (@var "ii" tptp.term)) % 175.23/175.52 (define @t229 () (@const 10 (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 175.23/175.52 (define @t230 () (@const 11 (-> (@ho-elim-sort (-> tptp.term tptp.term tptp.term)) tptp.term (@ho-elim-sort (-> tptp.term tptp.term))))) % 175.23/175.52 (define @t231 () (@var "BOUND_VARIABLE_10166" (@ho-elim-sort (-> tptp.subst tptp.term tptp.term)))) % 175.23/175.52 (define @t232 () (@const 12 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.term)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.term))))) % 175.23/175.52 (define @t233 () (@const 13 (-> (@ho-elim-sort (-> tptp.term tptp.term)) tptp.term tptp.term))) % 175.23/175.52 (define @t234 () (_ @t233 (_ @t232 @t231 @t108) @t107)) % 175.23/175.52 (define @t235 () (@var "BOUND_VARIABLE_10201" (@ho-elim-sort (-> tptp.subst tptp.term tptp.term)))) % 175.23/175.52 (define @t236 () (_ @t233 (_ @t232 @t235 @t108) @t107)) % 175.23/175.52 (define @t237 () (@const 14 (@ho-elim-sort (-> tptp.term tptp.term)))) % 175.23/175.52 (define @t238 () (_ @t233 @t237 (_ @t233 (_ @t232 @t231 @t207) @t210))) % 175.23/175.52 (define @t239 () (_ @t233 @t237 (_ @t233 (_ @t232 @t235 @t207) @t210))) % 175.23/175.52 (define @t240 () (_ @t213 (_ @t212 @t211 (_ @t233 (_ @t232 @t235 @t16) @t8)) @t13)) % 175.23/175.52 (define @t241 () (_ @t213 (_ @t212 @t211 @t8) @t13)) % 175.23/175.52 (define @t242 () (_ @t218 (_ @t217 @t216 @t16) @t13)) % 175.23/175.52 (define @t243 () (_ @t233 (_ @t232 @t235 @t242) @t241)) % 175.23/175.52 (define @t244 () (_ @t213 (_ @t212 @t211 (_ @t233 (_ @t232 @t231 @t16) @t8)) @t13)) % 175.23/175.52 (define @t245 () (_ @t233 (_ @t232 @t231 @t242) @t241)) % 175.23/175.52 (define @t246 () (not (forall @t23 (= @t245 @t244)))) % 175.23/175.52 (define @t247 () (@list @t231 @t235 @t108 @t107)) % 175.23/175.52 (define @t248 () (forall @t247 (or @t246 (not (forall @t23 (= @t243 @t240))) (not (= @t239 @t238)) (= @t236 @t234)))) % 175.23/175.52 (define @t249 () (@quantifiers_skolemize @t248 1)) % 175.23/175.52 (define @t250 () (_ @t232 @t249 @t207)) % 175.23/175.52 (define @t251 () (_ @t233 @t250 @t210)) % 175.23/175.52 (define @t252 () (@var "v" (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 175.23/175.52 (define @t253 () (@quantifiers_skolemize (forall (@list @t227) (= (_ @t230 @t229 @t227) (_ @t230 (@quantifiers_skolemize (forall (@list @t252) (not (forall (@list @t228) (= (_ @t230 @t252 @t228) (ite (= @t228 @t251) (_ @t230 @t229 @t210) (_ @t230 @t229 @t228)))))) 0) @t227))) 0)) % 175.23/175.52 (define @t254 () (not (= @t253 @t221))) % 175.23/175.52 (define @t255 () (forall @t174 @t254)) % 175.23/175.52 (define @t256 () (not @t255)) % 175.23/175.52 (define @t257 () (forall @t174 (not (= @t221 @t253)))) % 175.23/175.52 (define @t258 () (not @t257)) % 175.23/175.52 (define @t259 () (@list false)) % 175.23/175.52 (define @t260 () (@list @t222)) % 175.23/175.52 (define @t261 () (@quantifiers_skolemize @t257 0)) % 175.23/175.52 (define @t262 () (_ @t209 @t208 @t261)) % 175.23/175.52 (define @t263 () (= @t253 @t262)) % 175.23/175.52 (define @t264 () (= @t262 @t253)) % 175.23/175.52 (define @t265 () (not (not @t264))) % 175.23/175.52 (define @t266 () (@list true)) % 175.23/175.52 (define @t267 () (@list @t257)) % 175.23/175.52 (define @t268 () (_ @t206 @t205 @t162)) % 175.23/175.52 (define @t269 () (forall @t169 (not (forall @t163 (not (= @t166 @t268)))))) % 175.23/175.52 (define @t270 () (tptp.d2subst @t162)) % 175.23/175.52 (define @t271 () (not @t167)) % 175.23/175.52 (define @t272 () (forall @t163 @t271)) % 175.23/175.52 (define @t273 () (not @t272)) % 175.23/175.52 (define @t274 () (@var "BOUND_VARIABLE_9085" tptp.term)) % 175.23/175.52 (define @t275 () (@var "BOUND_VARIABLE_9083" tptp.subst)) % 175.23/175.52 (define @t276 () (_ @t233 (_ @t232 @t231 @t275) @t274)) % 175.23/175.52 (define @t277 () (@var "BOUND_VARIABLE_10161" (@ho-elim-sort (-> tptp.subst tptp.term tptp.term)))) % 175.23/175.52 (define @t278 () (_ @t233 (_ @t232 @t277 @t275) @t274)) % 175.23/175.52 (define @t279 () (_ @t213 (_ @t212 @t211 (_ @t233 (_ @t232 @t277 @t16) @t8)) @t13)) % 175.23/175.52 (define @t280 () (_ @t233 (_ @t232 @t277 @t242) @t241)) % 175.23/175.52 (define @t281 () (@list @t231 @t277 @t275 @t274)) % 175.23/175.52 (define @t282 () (forall @t281 (or @t246 (not (forall @t23 (= @t280 @t279))) (= @t278 @t276)))) % 175.23/175.52 (define @t283 () (@quantifiers_skolemize @t282 2)) % 175.23/175.52 (define @t284 () (not (= @t283 @t268))) % 175.23/175.52 (define @t285 () (forall @t163 @t284)) % 175.23/175.52 (define @t286 () (not @t285)) % 175.23/175.52 (define @t287 () (forall @t163 (not (= @t268 @t283)))) % 175.23/175.52 (define @t288 () (not @t287)) % 175.23/175.52 (define @t289 () (@list @t269)) % 175.23/175.52 (define @t290 () (@quantifiers_skolemize @t287 0)) % 175.23/175.52 (define @t291 () (_ @t206 @t205 @t290)) % 175.23/175.52 (define @t292 () (= @t283 @t291)) % 175.23/175.52 (define @t293 () (= @t291 @t283)) % 175.23/175.52 (define @t294 () (not (not @t293))) % 175.23/175.52 (define @t295 () (@quantifiers_skolemize @t282 3)) % 175.23/175.52 (define @t296 () (not (= @t295 @t221))) % 175.23/175.52 (define @t297 () (forall @t174 @t296)) % 175.23/175.52 (define @t298 () (not @t297)) % 175.23/175.52 (define @t299 () (forall @t174 (not (= @t221 @t295)))) % 175.23/175.52 (define @t300 () (not @t299)) % 175.23/175.52 (define @t301 () (@quantifiers_skolemize @t299 0)) % 175.23/175.52 (define @t302 () (_ @t209 @t208 @t301)) % 175.23/175.52 (define @t303 () (= @t295 @t302)) % 175.23/175.52 (define @t304 () (= @t302 @t295)) % 175.23/175.52 (define @t305 () (not (not @t304))) % 175.23/175.52 (define @t306 () (@quantifiers_skolemize @t282 0)) % 175.23/175.52 (define @t307 () (_ @t233 (_ @t232 @t306 @t283) @t295)) % 175.23/175.52 (define @t308 () (forall @t174 (not (= @t221 @t307)))) % 175.23/175.52 (define @t309 () (@quantifiers_skolemize @t308 0)) % 175.23/175.52 (define @t310 () (not (= @t307 @t221))) % 175.23/175.52 (define @t311 () (forall @t174 @t310)) % 175.23/175.52 (define @t312 () (not @t311)) % 175.23/175.52 (define @t313 () (not @t308)) % 175.23/175.52 (define @t314 () (_ @t209 @t208 @t309)) % 175.23/175.52 (define @t315 () (= @t307 @t314)) % 175.23/175.52 (define @t316 () (= @t314 @t307)) % 175.23/175.52 (define @t317 () (not (not @t316))) % 175.23/175.52 (define @t318 () (@var "z" tptp.term)) % 175.23/175.52 (define @t319 () (@var "ii" tptp.term)) % 175.23/175.52 (define @t320 () (_ (@const 16 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.subst Bool)))) (@const 15 (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool))) @t207)) % 175.23/175.52 (define @t321 () (@const 17 (-> (@ho-elim-sort (-> tptp.term tptp.subst Bool)) tptp.term (@ho-elim-sort (-> tptp.subst Bool))))) % 175.23/175.52 (define @t322 () (@var "v" (@ho-elim-sort (-> tptp.term tptp.subst Bool)))) % 175.23/175.52 (define @t323 () (@quantifiers_skolemize (forall (@list @t318) (= (_ @t321 @t320 @t318) (_ @t321 (@quantifiers_skolemize (forall (@list @t322) (not (forall (@list @t319) (= (_ @t321 @t322 @t319) (ite (= @t319 @t251) (_ @t321 @t320 @t210) (_ @t321 @t320 @t319)))))) 0) @t318))) 0)) % 175.23/175.52 (define @t324 () (forall @t174 (not (= @t221 @t323)))) % 175.23/175.52 (define @t325 () (@quantifiers_skolemize @t324 0)) % 175.23/175.52 (define @t326 () (not (= @t323 @t221))) % 175.23/175.52 (define @t327 () (forall @t174 @t326)) % 175.23/175.52 (define @t328 () (not @t327)) % 175.23/175.52 (define @t329 () (not @t324)) % 175.23/175.52 (define @t330 () (_ @t209 @t208 @t325)) % 175.23/175.52 (define @t331 () (= @t323 @t330)) % 175.23/175.52 (define @t332 () (= @t330 @t323)) % 175.23/175.52 (define @t333 () (not (not @t332))) % 175.23/175.52 (define @t334 () (@list @t324)) % 175.23/175.52 (define @t335 () (@var "z" tptp.term)) % 175.23/175.52 (define @t336 () (@var "ii" tptp.term)) % 175.23/175.52 (define @t337 () (@const 18 (@ho-elim-sort (-> tptp.term Bool)))) % 175.23/175.52 (define @t338 () (@const 19 (-> (@ho-elim-sort (-> tptp.term Bool)) tptp.term Bool))) % 175.23/175.52 (define @t339 () (@var "v" (@ho-elim-sort (-> tptp.term Bool)))) % 175.23/175.52 (define @t340 () (@quantifiers_skolemize (forall (@list @t335) (= (_ @t338 @t337 @t335) (_ @t338 (@quantifiers_skolemize (forall (@list @t339) (not (forall (@list @t336) (= (_ @t338 @t339 @t336) (ite (= @t210 @t336) (_ @t338 @t337 @t210) (_ @t338 @t337 @t336)))))) 0) @t335))) 0)) % 175.23/175.52 (define @t341 () (forall @t174 (not (= @t221 @t340)))) % 175.23/175.52 (define @t342 () (@quantifiers_skolemize @t341 0)) % 175.23/175.52 (define @t343 () (not (= @t340 @t221))) % 175.23/175.52 (define @t344 () (forall @t174 @t343)) % 175.23/175.52 (define @t345 () (not @t344)) % 175.23/175.52 (define @t346 () (not @t341)) % 175.23/175.52 (define @t347 () (_ @t209 @t208 @t342)) % 175.23/175.52 (define @t348 () (= @t340 @t347)) % 175.23/175.52 (define @t349 () (= @t347 @t340)) % 175.23/175.52 (define @t350 () (not (not @t349))) % 175.23/175.52 (define @t351 () (@quantifiers_skolemize @t248 3)) % 175.23/175.52 (define @t352 () (@quantifiers_skolemize @t248 2)) % 175.23/175.52 (define @t353 () (not (= @t352 @t268))) % 175.23/175.52 (define @t354 () (forall @t163 @t353)) % 175.23/175.52 (define @t355 () (not @t354)) % 175.23/175.52 (define @t356 () (forall @t163 (not (= @t268 @t352)))) % 175.23/175.52 (define @t357 () (not @t356)) % 175.23/175.52 (define @t358 () (@quantifiers_skolemize @t356 0)) % 175.23/175.52 (define @t359 () (_ @t206 @t205 @t358)) % 175.23/175.52 (define @t360 () (= @t352 @t359)) % 175.23/175.52 (define @t361 () (= @t359 @t352)) % 175.23/175.52 (define @t362 () (not (not @t361))) % 175.23/175.52 (define @t363 () (@quantifiers_skolemize @t248 0)) % 175.23/175.52 (define @t364 () (_ @t232 @t363 @t219)) % 175.23/175.52 (define @t365 () (_ @t232 @t363 @t207)) % 175.23/175.52 (define @t366 () (not (= @t351 @t221))) % 175.23/175.52 (define @t367 () (forall @t174 @t366)) % 175.23/175.52 (define @t368 () (not @t367)) % 175.23/175.52 (define @t369 () (forall @t174 (not (= @t221 @t351)))) % 175.23/175.52 (define @t370 () (not @t369)) % 175.23/175.52 (define @t371 () (@quantifiers_skolemize @t369 0)) % 175.23/175.52 (define @t372 () (_ @t209 @t208 @t371)) % 175.23/175.52 (define @t373 () (= @t351 @t372)) % 175.23/175.52 (define @t374 () (= @t372 @t351)) % 175.23/175.52 (define @t375 () (not (not @t374))) % 175.23/175.52 (define @t376 () (_ @t233 @t365 @t210)) % 175.23/175.52 (define @t377 () (not (= @t376 @t221))) % 175.23/175.52 (define @t378 () (forall @t174 @t377)) % 175.23/175.52 (define @t379 () (not @t378)) % 175.23/175.52 (define @t380 () (forall @t174 (not (= @t221 @t376)))) % 175.23/175.52 (define @t381 () (not @t380)) % 175.23/175.52 (define @t382 () (@quantifiers_skolemize @t380 0)) % 175.23/175.52 (define @t383 () (_ @t209 @t208 @t382)) % 175.23/175.52 (define @t384 () (= @t376 @t383)) % 175.23/175.52 (define @t385 () (= @t383 @t376)) % 175.23/175.52 (define @t386 () (not (not @t385))) % 175.23/175.52 (define @t387 () (forall @t174 (not (= @t221 @t251)))) % 175.23/175.52 (define @t388 () (@quantifiers_skolemize @t387 0)) % 175.23/175.52 (define @t389 () (_ @t209 @t208 @t388)) % 175.23/175.52 (define @t390 () (not (= @t251 @t221))) % 175.23/175.52 (define @t391 () (forall @t174 @t390)) % 175.23/175.52 (define @t392 () (not @t391)) % 175.23/175.52 (define @t393 () (not @t387)) % 175.23/175.52 (define @t394 () (= @t251 @t389)) % 175.23/175.52 (define @t395 () (= @t389 @t251)) % 175.23/175.52 (define @t396 () (not (not @t395))) % 175.23/175.52 (define @t397 () (_ @t232 @t249 @t219)) % 175.23/175.52 (define @t398 () (_ @t232 @t249 @t352)) % 175.23/175.52 (define @t399 () (_ @t233 @t398 @t351)) % 175.23/175.52 (define @t400 () (= @t399 (_ @t233 (_ @t232 @t363 @t352) @t351))) % 175.23/175.52 (define @t401 () (or (not (forall @t23 (= (_ @t233 (_ @t232 @t363 @t242) @t241) (_ @t213 (_ @t212 @t211 (_ @t233 (_ @t232 @t363 @t16) @t8)) @t13)))) (not (forall @t23 (= (_ @t233 (_ @t232 @t249 @t242) @t241) (_ @t213 (_ @t212 @t211 (_ @t233 (_ @t232 @t249 @t16) @t8)) @t13)))) (not (= (_ @t233 @t237 @t251) (_ @t233 @t237 @t376))) @t400)) % 175.23/175.52 (define @t402 () (not @t401)) % 175.23/175.52 (define @t403 () (not @t248)) % 175.23/175.52 (define @t404 () (not (= @t238 @t239))) % 175.23/175.52 (define @t405 () (forall @t23 (= @t240 @t243))) % 175.23/175.52 (define @t406 () (not @t405)) % 175.23/175.52 (define @t407 () (forall @t23 (= @t244 @t245))) % 175.23/175.52 (define @t408 () (not @t407)) % 175.23/175.52 (define @t409 () (or @t408 @t406 @t404 (= @t234 @t236))) % 175.23/175.52 (define @t410 () (forall @t247 @t409)) % 175.23/175.52 (define @t411 () (forall @t23 (= @t279 @t280))) % 175.23/175.52 (define @t412 () (not @t411)) % 175.23/175.52 (define @t413 () (or @t408 @t412 (= @t276 @t278))) % 175.23/175.52 (define @t414 () (forall @t281 @t413)) % 175.23/175.52 (define @t415 () (not (= @t410 @t414))) % 175.23/175.52 (define @t416 () (@var "BOUND_VARIABLE_9081" (-> tptp.subst tptp.term tptp.term))) % 175.23/175.52 (define @t417 () (= (_ @t4 @t275 @t274) (_ @t416 @t275 @t274))) % 175.23/175.52 (define @t418 () (tptp.sub @t8 @t13)) % 175.23/175.52 (define @t419 () (tptp.comp @t16 @t13)) % 175.23/175.52 (define @t420 () (not (forall @t23 (= (tptp.sub (_ @t416 @t16 @t8) @t13) (_ @t416 @t419 @t418))))) % 175.23/175.52 (define @t421 () (_ @t4 @t419 @t418)) % 175.23/175.52 (define @t422 () (_ @t4 @t16 @t8)) % 175.23/175.52 (define @t423 () (tptp.sub @t422 @t13)) % 175.23/175.52 (define @t424 () (forall @t23 (= @t423 @t421))) % 175.23/175.52 (define @t425 () (not @t424)) % 175.23/175.52 (define @t426 () (or @t425 @t420 @t417)) % 175.23/175.52 (define @t427 () (@list @t4 @t416 @t275 @t274)) % 175.23/175.52 (define @t428 () (_ @t109 @t108 @t107)) % 175.23/175.52 (define @t429 () (_ @t4 @t108 @t107)) % 175.23/175.52 (define @t430 () (= @t429 @t428)) % 175.23/175.52 (define @t431 () (tptp.d2term tptp.d_one)) % 175.23/175.52 (define @t432 () (tptp.d2subst tptp.d_id)) % 175.23/175.52 (define @t433 () (_ @t109 @t419 @t418)) % 175.23/175.52 (define @t434 () (_ @t109 @t16 @t8)) % 175.23/175.52 (define @t435 () (tptp.sub @t434 @t13)) % 175.23/175.52 (define @t436 () (not (forall @t23 (= @t435 @t433)))) % 175.23/175.52 (define @t437 () (forall @t124 (or @t425 @t436 (not (= (tptp.lam (_ @t4 @t432 @t431)) (tptp.lam (_ @t109 @t432 @t431)))) @t430))) % 175.23/175.52 (define @t438 () (_ @t157 @t83 @t416)) % 175.23/175.52 (define @t439 () (_ @t157 @t83 @t4)) % 175.23/175.52 (define @t440 () (= @t439 @t438)) % 175.23/175.52 (define @t441 () (not @t440)) % 175.23/175.52 (define @t442 () (or @t425 @t420 @t441 @t417)) % 175.23/175.52 (define @t443 () (forall @t427 @t442)) % 175.23/175.52 (define @t444 () (= @t437 @t443)) % 175.23/175.52 (define @t445 () (tptp.hoaslam tptp.id @t4)) % 175.23/175.52 (define @t446 () (= @t445 (tptp.hoaslam tptp.id @t416))) % 175.23/175.52 (define @t447 () (not @t446)) % 175.23/175.52 (define @t448 () (or @t425 @t420 @t447 @t417)) % 175.23/175.52 (define @t449 () (forall @t427 @t448)) % 175.23/175.52 (define @t450 () (_ @t109 @t83 @t84)) % 175.23/175.52 (define @t451 () (tptp.lam @t450)) % 175.23/175.52 (define @t452 () (_ @t4 @t83 @t84)) % 175.23/175.52 (define @t453 () (tptp.lam @t452)) % 175.23/175.52 (define @t454 () (= @t453 @t451)) % 175.23/175.52 (define @t455 () (not @t454)) % 175.23/175.52 (define @t456 () (or @t425 @t436 @t455 @t430)) % 175.23/175.52 (define @t457 () (forall @t124 @t456)) % 175.23/175.52 (define @t458 () (_ @t109 tptp.sh tptp.one)) % 175.23/175.52 (define @t459 () (tptp.lam @t458)) % 175.23/175.52 (define @t460 () (_ @t4 tptp.sh tptp.one)) % 175.23/175.52 (define @t461 () (tptp.lam @t460)) % 175.23/175.52 (define @t462 () (= @t461 @t459)) % 175.23/175.52 (define @t463 () (not @t462)) % 175.23/175.52 (define @t464 () (or @t425 @t436 @t463 @t430)) % 175.23/175.52 (define @t465 () (forall @t124 @t464)) % 175.23/175.52 (define @t466 () (or @t425 @t436 @t116 @t112)) % 175.23/175.52 (define @t467 () (= tptp.hoaslaminj @t449)) % 175.23/175.52 (define @t468 () (or @t420 @t447 @t417)) % 175.23/175.52 (define @t469 () (or @t425 @t468)) % 175.23/175.52 (define @t470 () (forall @t427 @t469)) % 175.23/175.52 (define @t471 () (@list @t416 @t275 @t274)) % 175.23/175.52 (define @t472 () (forall @t471 @t469)) % 175.23/175.52 (define @t473 () (forall @t471 @t468)) % 175.23/175.52 (define @t474 () (@var "BOUND_VARIABLE_9069" tptp.term)) % 175.23/175.52 (define @t475 () (@var "BOUND_VARIABLE_9067" tptp.subst)) % 175.23/175.52 (define @t476 () (or @t425 @t473)) % 175.23/175.52 (define @t477 () (= (_ @t4 @t475 @t474) (_ @t182 @t475 @t474))) % 175.23/175.52 (define @t478 () (not (= @t445 (tptp.hoaslam tptp.id @t182)))) % 175.23/175.52 (define @t479 () (_ @t182 @t419 @t418)) % 175.23/175.52 (define @t480 () (_ @t182 @t16 @t8)) % 175.23/175.52 (define @t481 () (tptp.sub @t480 @t13)) % 175.23/175.52 (define @t482 () (forall @t23 (= @t481 @t479))) % 175.23/175.52 (define @t483 () (not @t482)) % 175.23/175.52 (define @t484 () (or @t483 @t478 @t477)) % 175.23/175.52 (define @t485 () (forall (@list @t182 @t475 @t474) @t484)) % 175.23/175.52 (define @t486 () (@list @t475 @t474)) % 175.23/175.52 (define @t487 () (forall @t486 @t484)) % 175.23/175.52 (define @t488 () (forall @t486 @t477)) % 175.23/175.52 (define @t489 () (or @t483 @t478 @t488)) % 175.23/175.52 (define @t490 () (forall @t185 (= @t422 @t480))) % 175.23/175.52 (define @t491 () (lambda @t185 @t480)) % 175.23/175.52 (define @t492 () (tptp.hoaslam tptp.id @t491)) % 175.23/175.52 (define @t493 () (lambda @t185 @t422)) % 175.23/175.52 (define @t494 () (tptp.hoaslam tptp.id @t493)) % 175.23/175.52 (define @t495 () (= @t494 @t492)) % 175.23/175.52 (define @t496 () (not @t495)) % 175.23/175.52 (define @t497 () (or @t483 @t496 @t490)) % 175.23/175.52 (define @t498 () (not @t192)) % 175.23/175.52 (define @t499 () (or @t483 @t498 @t490)) % 175.23/175.52 (define @t500 () (=> @t192 @t490)) % 175.23/175.52 (define @t501 () (not @t282)) % 175.23/175.52 (define @t502 () (@quantifiers_skolemize @t282 1)) % 175.23/175.52 (define @t503 () (_ @t232 @t502 @t283)) % 175.23/175.52 (define @t504 () (_ @t233 @t503 @t295)) % 175.23/175.52 (define @t505 () (= @t504 @t307)) % 175.23/175.52 (define @t506 () (or (not (forall @t23 (= (_ @t233 (_ @t232 @t306 @t242) @t241) (_ @t213 (_ @t212 @t211 (_ @t233 (_ @t232 @t306 @t16) @t8)) @t13)))) (not (forall @t23 (= (_ @t233 (_ @t232 @t502 @t242) @t241) (_ @t213 (_ @t212 @t211 (_ @t233 (_ @t232 @t502 @t16) @t8)) @t13)))) @t505)) % 175.23/175.52 (define @t507 () (not @t506)) % 175.23/175.52 (define @t508 () (not @t505)) % 175.23/175.52 (define @t509 () (_ @t232 @t502 @t207)) % 175.23/175.52 (define @t510 () (_ @t233 @t509 @t210)) % 175.23/175.52 (define @t511 () (= @t253 @t510)) % 175.23/175.52 (define @t512 () (not @t511)) % 175.23/175.52 (define @t513 () (= tptp.d_one @t309)) % 175.23/175.52 (define @t514 () (not @t513)) % 175.23/175.52 (define @t515 () (not @t315)) % 175.23/175.52 (define @t516 () (= tptp.d_one @t301)) % 175.23/175.52 (define @t517 () (not @t516)) % 175.23/175.52 (define @t518 () (not @t303)) % 175.23/175.52 (define @t519 () (= tptp.d_one @t325)) % 175.23/175.52 (define @t520 () (not @t519)) % 175.23/175.52 (define @t521 () (not @t331)) % 175.23/175.52 (define @t522 () (= tptp.d_id @t290)) % 175.23/175.52 (define @t523 () (not @t522)) % 175.23/175.52 (define @t524 () (not @t292)) % 175.23/175.52 (define @t525 () (= tptp.d_one @t261)) % 175.23/175.52 (define @t526 () (not @t525)) % 175.23/175.52 (define @t527 () (not @t263)) % 175.23/175.52 (define @t528 () (= tptp.d_one @t342)) % 175.23/175.52 (define @t529 () (not @t528)) % 175.23/175.52 (define @t530 () (not @t348)) % 175.23/175.52 (define @t531 () (= tptp.d_one @t388)) % 175.23/175.52 (define @t532 () (not @t531)) % 175.23/175.52 (define @t533 () (not @t394)) % 175.23/175.52 (define @t534 () (not @t220)) % 175.23/175.52 (define @t535 () (not @t215)) % 175.23/175.52 (define @t536 () (= @t307 @t510)) % 175.23/175.52 (define @t537 () (not @t536)) % 175.23/175.52 (define @t538 () (= @t510 @t307)) % 175.23/175.52 (define @t539 () (_ @t233 @t509 @t295)) % 175.23/175.52 (define @t540 () (_ @t232 @t502 @t219)) % 175.23/175.52 (define @t541 () (_ @t233 @t540 @t214)) % 175.23/175.52 (define @t542 () (and @t215 @t220 @t394 @t531 @t508 @t348 @t528 @t263 @t525 @t292 @t522 @t331 @t519 @t303 @t516 @t315 @t513)) % 175.23/175.52 (define @t543 () (not (= @t504 @t221))) % 175.23/175.52 (define @t544 () (forall @t174 @t543)) % 175.23/175.52 (define @t545 () (not @t544)) % 175.23/175.52 (define @t546 () (forall @t174 (not (= @t221 @t504)))) % 175.23/175.52 (define @t547 () (not @t546)) % 175.23/175.52 (define @t548 () (@quantifiers_skolemize @t546 0)) % 175.23/175.52 (define @t549 () (_ @t209 @t208 @t548)) % 175.23/175.52 (define @t550 () (= @t504 @t549)) % 175.23/175.52 (define @t551 () (= @t549 @t504)) % 175.23/175.52 (define @t552 () (not (not @t551))) % 175.23/175.52 (define @t553 () (= tptp.d_one @t548)) % 175.23/175.52 (define @t554 () (and @t215 @t220 @t263 @t525 @t292 @t522 @t303 @t516 @t550 @t553)) % 175.23/175.52 (assume @p1 (and @t181 @t175 (forall (@list @t172 @t171) (=> (= (_ tptp.d2term @t172) (_ tptp.d2term @t171)) (= @t172 @t171))) @t170 @t164 (forall (@list @t161 @t160) (=> (= (_ tptp.d2subst @t161) (_ tptp.d2subst @t160)) (= @t161 @t160))) (= tptp.one @t84) (= (_ (_ tptp.ap @t84) @t84) @t84) (= (_ tptp.lam @t84) @t84) (= @t159 @t84) (= tptp.id @t83) (= tptp.sh @t83) (= (_ (_ tptp.push @t84) @t83) @t83) (= @t158 @t83) (= (_ (_ (_ (_ tptp.hoasap @t83) @t84) @t83) @t84) @t84) (= tptp.hoaslam @t157) (= tptp.hoasinduction_p_and_p_prime (lambda (@list @t2 @t42) @t50)) (= tptp.pushprop_p_and_p_prime (lambda (@list @t8 @t16 @t55 @t42) @t71)) (not (_ tptp.var @t84)) (= tptp.pushprop_lem1v2 @t140) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t32 (or (not (= (_ @t14 tptp.sh) (_ @t94 tptp.sh))) @t105))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t98) (= tptp.hoasinduction_lem3v2_f @t99) tptp.axvarshift (= tptp.hoasapinj2 @t134) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t130) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t80 (=> @t76 (=> @t90 (=> @t139 @t98))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t99) (= tptp.hoasinduction_lthm (=> @t65 (=> @t143 (=> @t101 @t40)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t67 (=> @t65 (=> @t53 (=> @t52 @t86))))) @t156 (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t144) (or (not (forall (@list @t4 @t151) (or @t12 @t7 (not (forall (@list @t154 @t155 @t153) (= (_ (_ tptp.sub (_ (_ @t4 @t154) @t155)) @t153) (_ (_ tptp.sub (_ @t152 (_ (_ tptp.push @t155) @t154))) @t153)))) (not (forall (@list @t147 @t149 @t146) (= (_ (_ @t4 @t148) @t150) (_ @t152 (_ (_ tptp.push @t150) @t148)))))))) (not (forall @t46 (or @t31 (_ (_ @t3 (_ @t145 @t44)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t145 @t93))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t104) (= tptp.hoasinduction_lem3 @t101) (= tptp.hoasinduction_lem2 @t143) (= tptp.termmset_lthm (=> @t53 @t53)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t80 @t140)) tptp.hoasapnotvar (= tptp.hoasinduction_lem0 @t67) (= tptp.hoasinduction @t40) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t95) tptp.ulamvarind (= tptp.induction @t139) (= tptp.hoasinduction_lem3a_lthm (=> @t53 (=> @t104 @t88))) tptp.termmset_gthm (= tptp.hoasinduction_lem3aa @t104) 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 @t42 @t137 @t136) (or @t39 @t38 @t33 @t51 (not (_ @t42 @t137)) (not (_ @t42 @t136)) (_ @t42 (_ (_ tptp.ap @t137) @t136))))) tptp.pushprop_lthm (= tptp.apinj2 @t135) (= tptp.apinj1 @t132) (= tptp.hoasapinj2_lthm (=> @t135 @t134)) (= tptp.hoasinduction_lem3v2a @t52) (= tptp.hoasapinj1_lthm (=> @t53 (=> @t132 @t130))) (= tptp.hoaslaminj_lthm (=> @t80 (=> @t76 (=> @t106 @t125)))) (= tptp.axvarcons @t80) (= tptp.axscons (forall @t89 (= @t16 (_ (_ tptp.push (_ @t79 @t16)) (_ @t74 @t16))))) tptp.hoasinduction_lem2v2_gthm (= tptp.axidr @t90) (= tptp.pushprop_lem1 @t78) (= tptp.laminj @t106) (= tptp.hoasinduction_lem3_lthm (=> @t53 (=> @t104 @t101))) (= tptp.pushprop_lem0 @t73) tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t99 (=> @t53 @t52))) tptp.hoasinduction_lem2_lthm tptp.hoasapinj2_gthm tptp.hoasinduction_lem1_lthm (not tptp.lamnotap) tptp.hoasapinj1_gthm tptp.hoaslamnotvar (= tptp.axidl @t91) tptp.hoaslaminj_gthm (= tptp.induction2_lthm (=> @t53 (=> @t98 @t65))) (= tptp.hoasinduction_lem0_lthm @t67) (= tptp.substmonoid_lthm (=> @t91 (=> @t90 @t92))) tptp.pushprop tptp.hoasinduction_lem3_gthm tptp.hoasinduction_lem2_gthm (= tptp.hoasinduction_lem3b @t95) (= tptp.substmonoid @t92) tptp.lamnotvar (= tptp.hoasinduction_lem3a @t88) tptp.hoasinduction_lem1_gthm (= tptp.hoasinduction_no_psi_cond @t86) tptp.induction2_gthm tptp.pushprop_lem2v2_lthm (not (_ (_ (_ tptp.hoasvar @t83) @t84) @t83)) (= tptp.hoaslamnotap (forall (@list @t4 @t82 @t81) (or @t25 (not (= @t6 (_ (_ tptp.ap (_ (_ tptp.sub @t82) tptp.id)) @t81)))))) tptp.substmonoid_gthm tptp.ulamvarsh (= tptp.induction2 @t65) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t80 (=> @t76 @t78))) (= tptp.hoasinduction_lem3v2 @t69) (= tptp.axshiftcons @t76) (= tptp.termmset @t53) (= tptp.pushprop_lem0_lthm @t73) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t53 @t69)) (= tptp.axvarid @t53) (= tptp.hoasinduction_lthm_3 (=> @t67 (=> @t65 (=> @t53 (=> @t52 @t40))))))) % 175.23/175.52 (assume @p2 @t204) % 175.23/175.52 (assume @p3 true) % 175.23/175.52 ; WARNING: add trust step for TRUST % 175.23/175.52 ; trust TRUST PREPROCESS_HO_ELIM % 175.23/175.52 (step @p4 :rule trust :premises () :args ((= (= @t84 @t159) @t215))) % 175.23/175.52 (step @p5 :rule eq-symm :args (@t159 @t84)) % 175.23/175.52 (step @p6 :rule trans :premises (@p5 @p4)) % 175.23/175.52 (step @p7 :rule and_elim :premises (@p1) :args (9)) % 175.23/175.52 (step @p8 :rule eq_resolve :premises (@p7 @p6)) % 175.23/175.52 ; trust TRUST PREPROCESS_HO_ELIM % 175.23/175.52 (step @p9 :rule trust :premises () :args ((= (= @t83 @t158) @t220))) % 175.23/175.52 (step @p10 :rule eq-symm :args (@t158 @t83)) % 175.23/175.52 (step @p11 :rule trans :premises (@p10 @p9)) % 175.23/175.52 (step @p12 :rule and_elim :premises (@p1) :args (13)) % 175.23/175.52 (step @p13 :rule eq_resolve :premises (@p12 @p11)) % 175.23/175.52 ; trust TRUST PREPROCESS_HO_ELIM % 175.23/175.52 (step @p14 :rule trust :premises () :args ((= (forall @t180 (not (forall @t174 (not (= @t177 @t223))))) @t222))) % 175.23/175.52 (step @p15 :rule refl :args (@t223)) % 175.23/175.52 (step @p16 :rule refl :args (@t176)) % 175.23/175.52 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t176 @t223))) % 175.23/175.52 (step @p18 :rule symm :premises (@p17)) % 175.23/175.52 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 175.23/175.52 (step @p20 :rule refl :args (@t177)) % 175.23/175.52 (step @p21 :rule cong :premises (@p20 @p19) :args (@t178)) % 175.23/175.52 (step @p22 :rule cong :premises (@p21) :args (@t224)) % 175.23/175.52 (step @p23 :rule cong :premises (@p22) :args (@t225)) % 175.23/175.52 (step @p24 :rule cong :premises (@p23) :args (@t226)) % 175.23/175.52 (step @p25 :rule exists-elim :args ((= @t179 @t226))) % 175.23/175.52 (step @p26 :rule trans :premises (@p25 @p24)) % 175.23/175.52 (step @p27 :rule cong :premises (@p26) :args (@t181)) % 175.23/175.52 (step @p28 :rule trans :premises (@p27 @p14)) % 175.23/175.52 (step @p29 :rule and_elim :premises (@p1) :args (0)) % 175.23/175.52 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 175.23/175.52 (step @p31 :rule eq-symm :args (@t253 @t221)) % 175.23/175.52 (step @p32 :rule cong :premises (@p31) :args (@t254)) % 175.23/175.52 (step @p33 :rule cong :premises (@p32) :args (@t255)) % 175.23/175.52 (step @p34 :rule cong :premises (@p33) :args (@t256)) % 175.23/175.52 (step @p35 :rule refl :args (@t222)) % 175.23/175.52 (step @p36 :rule cong :premises (@p35 @p34) :args ((=> @t222 @t256))) % 175.23/175.52 (assume-push @p986 @t222) % 175.23/175.52 (step @p38 :rule instantiate :premises (@p30) :args ((@list @t253))) % 175.23/175.52 (step-pop @p987 :rule scope :premises (@p38)) % 175.23/175.52 (step @p39 :rule process_scope :premises (@p987) :args (@t256)) % 175.23/175.52 (step @p41 :rule eq_resolve :premises (@p39 @p36)) % 175.23/175.52 (step @p42 :rule implies_elim :premises (@p41)) % 175.23/175.52 (step @p43 :rule chain_m_resolution :premises (@p42 @p30) :args (@t258 @t259 @t260)) % 175.23/175.52 (step @p44 :rule refl :args (@t263)) % 175.23/175.52 (step @p45 :rule bool-double-not-elim :args (@t257)) % 175.23/175.52 (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or (not @t258) @t263))) % 175.23/175.52 (step @p47 :rule eq-symm :args (@t262 @t253)) % 175.23/175.52 (step @p48 :rule bool-double-not-elim :args (@t264)) % 175.23/175.52 (step @p49 :rule trans :premises (@p48 @p47)) % 175.23/175.52 (step @p50 :rule refl :args (@t258)) % 175.23/175.52 (step @p51 :rule cong :premises (@p50 @p49) :args ((=> @t258 @t265))) % 175.23/175.52 (assume-push @p988 @t258) % 175.23/175.52 (step @p53 :rule skolemize :premises (@p43)) % 175.23/175.52 (step-pop @p989 :rule scope :premises (@p53)) % 175.23/175.52 (step @p54 :rule process_scope :premises (@p989) :args (@t265)) % 175.23/175.52 (step @p56 :rule eq_resolve :premises (@p54 @p51)) % 175.23/175.52 (step @p57 :rule implies_elim :premises (@p56)) % 175.23/175.52 (step @p58 :rule eq_resolve :premises (@p57 @p46)) % 175.23/175.52 (step @p59 :rule chain_m_resolution :premises (@p58 @p43) :args (@t263 @t266 @t267)) % 175.23/175.52 (step @p60 :rule eq-symm :args (@t173 tptp.d_one)) % 175.23/175.52 (step @p61 :rule cong :premises (@p60) :args (@t175)) % 175.23/175.52 (step @p62 :rule and_elim :premises (@p1) :args (1)) % 175.23/175.52 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 175.23/175.52 (step @p64 :rule instantiate :premises (@p63) :args ((@list @t261))) % 175.23/175.52 ; trust TRUST PREPROCESS_HO_ELIM % 175.23/175.52 (step @p65 :rule trust :premises () :args ((= (forall @t169 (not (forall @t163 (not (= @t166 @t270))))) @t269))) % 175.23/175.52 (step @p66 :rule refl :args (@t270)) % 175.23/175.52 (step @p67 :rule refl :args (@t165)) % 175.23/175.52 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t165 @t270))) % 175.23/175.52 (step @p69 :rule symm :premises (@p68)) % 175.23/175.52 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 175.23/175.52 (step @p71 :rule refl :args (@t166)) % 175.23/175.52 (step @p72 :rule cong :premises (@p71 @p70) :args (@t167)) % 175.23/175.52 (step @p73 :rule cong :premises (@p72) :args (@t271)) % 175.23/175.52 (step @p74 :rule cong :premises (@p73) :args (@t272)) % 175.23/175.52 (step @p75 :rule cong :premises (@p74) :args (@t273)) % 175.23/175.52 (step @p76 :rule exists-elim :args ((= @t168 @t273))) % 175.23/175.52 (step @p77 :rule trans :premises (@p76 @p75)) % 175.23/175.52 (step @p78 :rule cong :premises (@p77) :args (@t170)) % 175.23/175.52 (step @p79 :rule trans :premises (@p78 @p65)) % 175.23/175.52 (step @p80 :rule and_elim :premises (@p1) :args (3)) % 175.23/175.52 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 175.23/175.52 (step @p82 :rule eq-symm :args (@t283 @t268)) % 175.23/175.52 (step @p83 :rule cong :premises (@p82) :args (@t284)) % 175.23/175.52 (step @p84 :rule cong :premises (@p83) :args (@t285)) % 175.23/175.52 (step @p85 :rule cong :premises (@p84) :args (@t286)) % 175.23/175.52 (step @p86 :rule refl :args (@t269)) % 175.23/175.52 (step @p87 :rule cong :premises (@p86 @p85) :args ((=> @t269 @t286))) % 175.23/175.52 (assume-push @p990 @t269) % 175.23/175.52 (step @p89 :rule instantiate :premises (@p81) :args ((@list @t283))) % 175.23/175.52 (step-pop @p991 :rule scope :premises (@p89)) % 175.23/175.52 (step @p90 :rule process_scope :premises (@p991) :args (@t286)) % 175.23/175.52 (step @p92 :rule eq_resolve :premises (@p90 @p87)) % 175.23/175.52 (step @p93 :rule implies_elim :premises (@p92)) % 175.23/175.52 (step @p94 :rule chain_m_resolution :premises (@p93 @p81) :args (@t288 @t259 @t289)) % 175.23/175.52 (step @p95 :rule refl :args (@t292)) % 175.23/175.52 (step @p96 :rule bool-double-not-elim :args (@t287)) % 175.23/175.52 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t288) @t292))) % 175.23/175.52 (step @p98 :rule eq-symm :args (@t291 @t283)) % 175.23/175.52 (step @p99 :rule bool-double-not-elim :args (@t293)) % 175.23/175.52 (step @p100 :rule trans :premises (@p99 @p98)) % 175.23/175.52 (step @p101 :rule refl :args (@t288)) % 175.23/175.52 (step @p102 :rule cong :premises (@p101 @p100) :args ((=> @t288 @t294))) % 175.23/175.52 (assume-push @p992 @t288) % 175.23/175.52 (step @p104 :rule skolemize :premises (@p94)) % 175.23/175.52 (step-pop @p993 :rule scope :premises (@p104)) % 175.23/175.52 (step @p105 :rule process_scope :premises (@p993) :args (@t294)) % 175.23/175.52 (step @p107 :rule eq_resolve :premises (@p105 @p102)) % 175.23/175.52 (step @p108 :rule implies_elim :premises (@p107)) % 175.23/175.52 (step @p109 :rule eq_resolve :premises (@p108 @p97)) % 175.23/175.52 (step @p110 :rule chain_m_resolution :premises (@p109 @p94) :args (@t292 @t266 (@list @t287))) % 175.23/175.52 (step @p111 :rule eq-symm :args (@t162 tptp.d_id)) % 175.23/175.52 (step @p112 :rule cong :premises (@p111) :args (@t164)) % 175.23/175.52 (step @p113 :rule and_elim :premises (@p1) :args (4)) % 175.23/175.52 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 175.23/175.52 (step @p115 :rule instantiate :premises (@p114) :args ((@list @t290))) % 175.23/175.52 (step @p116 :rule eq-symm :args (@t295 @t221)) % 175.23/175.52 (step @p117 :rule cong :premises (@p116) :args (@t296)) % 175.23/175.52 (step @p118 :rule cong :premises (@p117) :args (@t297)) % 175.23/175.52 (step @p119 :rule cong :premises (@p118) :args (@t298)) % 175.23/175.52 (step @p120 :rule cong :premises (@p35 @p119) :args ((=> @t222 @t298))) % 175.23/175.52 (assume-push @p994 @t222) % 175.23/175.52 (step @p122 :rule instantiate :premises (@p30) :args ((@list @t295))) % 175.23/175.52 (step-pop @p995 :rule scope :premises (@p122)) % 175.23/175.52 (step @p123 :rule process_scope :premises (@p995) :args (@t298)) % 175.23/175.52 (step @p125 :rule eq_resolve :premises (@p123 @p120)) % 175.23/175.52 (step @p126 :rule implies_elim :premises (@p125)) % 175.23/175.52 (step @p127 :rule chain_m_resolution :premises (@p126 @p30) :args (@t300 @t259 @t260)) % 175.23/175.52 (step @p128 :rule refl :args (@t303)) % 175.23/175.52 (step @p129 :rule bool-double-not-elim :args (@t299)) % 175.23/175.52 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or (not @t300) @t303))) % 175.23/175.52 (step @p131 :rule eq-symm :args (@t302 @t295)) % 175.23/175.52 (step @p132 :rule bool-double-not-elim :args (@t304)) % 175.23/175.52 (step @p133 :rule trans :premises (@p132 @p131)) % 175.23/175.52 (step @p134 :rule refl :args (@t300)) % 175.23/175.52 (step @p135 :rule cong :premises (@p134 @p133) :args ((=> @t300 @t305))) % 175.23/175.52 (assume-push @p996 @t300) % 175.23/175.52 (step @p137 :rule skolemize :premises (@p127)) % 175.23/175.52 (step-pop @p997 :rule scope :premises (@p137)) % 175.23/175.52 (step @p138 :rule process_scope :premises (@p997) :args (@t305)) % 175.23/175.52 (step @p140 :rule eq_resolve :premises (@p138 @p135)) % 175.23/175.52 (step @p141 :rule implies_elim :premises (@p140)) % 175.23/175.52 (step @p142 :rule eq_resolve :premises (@p141 @p130)) % 175.23/175.52 (step @p143 :rule chain_m_resolution :premises (@p142 @p127) :args (@t303 @t266 (@list @t299))) % 175.23/175.52 (step @p144 :rule instantiate :premises (@p63) :args ((@list @t301))) % 175.23/175.52 (step @p145 :rule instantiate :premises (@p63) :args ((@list @t309))) % 175.23/175.52 (step @p146 :rule eq-symm :args (@t307 @t221)) % 175.23/175.52 (step @p147 :rule cong :premises (@p146) :args (@t310)) % 175.23/175.52 (step @p148 :rule cong :premises (@p147) :args (@t311)) % 175.23/175.52 (step @p149 :rule cong :premises (@p148) :args (@t312)) % 175.23/175.52 (step @p150 :rule cong :premises (@p35 @p149) :args ((=> @t222 @t312))) % 175.23/175.52 (assume-push @p998 @t222) % 175.23/175.52 (step @p152 :rule instantiate :premises (@p30) :args ((@list @t307))) % 175.23/175.52 (step-pop @p999 :rule scope :premises (@p152)) % 175.23/175.52 (step @p153 :rule process_scope :premises (@p999) :args (@t312)) % 175.23/175.52 (step @p155 :rule eq_resolve :premises (@p153 @p150)) % 175.23/175.52 (step @p156 :rule implies_elim :premises (@p155)) % 175.23/175.52 (step @p157 :rule chain_m_resolution :premises (@p156 @p30) :args (@t313 @t259 @t260)) % 175.23/175.52 (step @p158 :rule refl :args (@t315)) % 175.23/175.52 (step @p159 :rule bool-double-not-elim :args (@t308)) % 175.23/175.52 (step @p160 :rule nary_cong :premises (@p159 @p158) :args ((or (not @t313) @t315))) % 175.23/175.52 (step @p161 :rule eq-symm :args (@t314 @t307)) % 175.23/175.52 (step @p162 :rule bool-double-not-elim :args (@t316)) % 175.23/175.52 (step @p163 :rule trans :premises (@p162 @p161)) % 175.23/175.52 (step @p164 :rule refl :args (@t313)) % 175.23/175.52 (step @p165 :rule cong :premises (@p164 @p163) :args ((=> @t313 @t317))) % 175.23/175.52 (assume-push @p1000 @t313) % 175.23/175.52 (step @p167 :rule skolemize :premises (@p157)) % 175.23/175.52 (step-pop @p1001 :rule scope :premises (@p167)) % 175.23/175.52 (step @p168 :rule process_scope :premises (@p1001) :args (@t317)) % 175.23/175.52 (step @p170 :rule eq_resolve :premises (@p168 @p165)) % 175.23/175.52 (step @p171 :rule implies_elim :premises (@p170)) % 175.23/175.52 (step @p172 :rule eq_resolve :premises (@p171 @p160)) % 175.23/175.52 (step @p173 :rule chain_m_resolution :premises (@p172 @p157) :args (@t315 @t266 (@list @t308))) % 175.23/175.52 (step @p174 :rule instantiate :premises (@p63) :args ((@list @t325))) % 175.23/175.52 (step @p175 :rule eq-symm :args (@t323 @t221)) % 175.23/175.52 (step @p176 :rule cong :premises (@p175) :args (@t326)) % 175.23/175.52 (step @p177 :rule cong :premises (@p176) :args (@t327)) % 175.23/175.52 (step @p178 :rule cong :premises (@p177) :args (@t328)) % 175.23/175.52 (step @p179 :rule cong :premises (@p35 @p178) :args ((=> @t222 @t328))) % 175.23/175.52 (assume-push @p1002 @t222) % 175.23/175.52 (step @p181 :rule instantiate :premises (@p30) :args ((@list @t323))) % 175.23/175.52 (step-pop @p1003 :rule scope :premises (@p181)) % 175.23/175.52 (step @p182 :rule process_scope :premises (@p1003) :args (@t328)) % 175.23/175.52 (step @p184 :rule eq_resolve :premises (@p182 @p179)) % 175.23/175.52 (step @p185 :rule implies_elim :premises (@p184)) % 175.23/175.52 (step @p186 :rule chain_m_resolution :premises (@p185 @p30) :args (@t329 @t259 @t260)) % 175.23/175.52 (step @p187 :rule refl :args (@t331)) % 175.23/175.52 (step @p188 :rule bool-double-not-elim :args (@t324)) % 175.23/175.52 (step @p189 :rule nary_cong :premises (@p188 @p187) :args ((or (not @t329) @t331))) % 175.23/175.52 (step @p190 :rule eq-symm :args (@t330 @t323)) % 175.23/175.52 (step @p191 :rule bool-double-not-elim :args (@t332)) % 175.23/175.52 (step @p192 :rule trans :premises (@p191 @p190)) % 175.23/175.52 (step @p193 :rule refl :args 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(@t415)) % 175.23/175.52 ; trust TRUST PREPROCESS_HO_ELIM % 175.23/175.52 (step @p415 :rule trust :premises () :args ((= (not (= @t437 (forall @t427 @t426))) @t415))) % 175.23/175.52 (step @p416 :rule aci_norm :args ((= (or @t425 @t420 false @t417) @t426))) % 175.23/175.52 (step @p417 :rule refl :args (@t417)) % 175.23/175.52 (step @p418 :rule evaluate :args ((not true))) % 175.23/175.52 (step @p419 :rule eq-refl :args (@t84)) % 175.23/175.52 (step @p420 :rule beta-reduce :args ((= @t438 @t84))) % 175.23/175.52 (step @p421 :rule beta-reduce :args ((= @t439 @t84))) % 175.23/175.52 (step @p422 :rule cong :premises (@p421 @p420) :args (@t440)) % 175.23/175.52 (step @p423 :rule trans :premises (@p422 @p419)) % 175.23/175.52 (step @p424 :rule cong :premises (@p423) :args (@t441)) % 175.23/175.52 (step @p425 :rule trans :premises (@p424 @p418)) % 175.23/175.52 (step @p426 :rule refl :args (@t420)) % 175.23/175.52 (step @p427 :rule refl :args (@t425)) % 175.23/175.52 (step @p428 :rule nary_cong :premises (@p427 @p426 @p425 @p417) :args (@t442)) % 175.23/175.52 (step @p429 :rule trans :premises (@p428 @p416)) % 175.23/175.52 (step @p430 :rule cong :premises (@p429) :args (@t443)) % 175.23/175.52 (step @p431 :rule refl :args (@t437)) % 175.23/175.52 (step @p432 :rule cong :premises (@p431 @p430) :args (@t444)) % 175.23/175.52 (step @p433 :rule cong :premises (@p432) :args ((not @t444))) % 175.23/175.52 (step @p434 :rule refl :args (@t416)) % 175.23/175.52 (step @p435 :rule and_elim :premises (@p1) :args (10)) % 175.23/175.52 (step @p436 :rule and_elim :premises (@p1) :args (15)) % 175.23/175.52 (step @p437 :rule ho_cong :premises (@p436 @p435 @p434)) % 175.23/175.52 (step @p438 :rule refl :args (@t4)) % 175.23/175.52 (step @p439 :rule ho_cong :premises (@p436 @p435 @p438)) % 175.23/175.52 (step @p440 :rule cong :premises (@p439 @p437) :args (@t446)) % 175.23/175.52 (step @p441 :rule cong :premises (@p440) :args (@t447)) % 175.23/175.52 (step @p442 :rule nary_cong :premises (@p427 @p426 @p441 @p417) :args (@t448)) % 175.23/175.52 (step @p443 :rule cong :premises (@p442) :args (@t449)) % 175.23/175.52 (step @p444 :rule refl :args (@t430)) % 175.23/175.52 (step @p445 :rule refl :args (@t431)) % 175.23/175.52 (step @p446 :rule refl :args (@t84)) % 175.23/175.52 (step @p447 :rule cong :premises (@p446 @p445) :args ((= @t84 @t431))) % 175.23/175.52 (step @p448 :rule symm :premises (@p447)) % 175.23/175.52 (step @p449 :rule eq_resolve :premises (@p446 @p448)) % 175.23/175.52 (step @p450 :rule refl :args (@t432)) % 175.23/175.52 (step @p451 :rule refl :args (@t83)) % 175.23/175.52 (step @p452 :rule cong :premises (@p451 @p450) :args ((= @t83 @t432))) % 175.23/175.52 (step @p453 :rule symm :premises (@p452)) % 175.23/175.52 (step @p454 :rule eq_resolve :premises (@p451 @p453)) % 175.23/175.52 (step @p455 :rule cong :premises (@p454 @p449) :args (@t450)) % 175.23/175.52 (step @p456 :rule cong :premises (@p455) :args (@t451)) % 175.23/175.52 (step @p457 :rule cong :premises (@p454 @p449) :args (@t452)) % 175.23/175.52 (step @p458 :rule cong :premises (@p457) :args (@t453)) % 175.23/175.52 (step @p459 :rule cong :premises (@p458 @p456) :args (@t454)) % 175.23/175.52 (step @p460 :rule cong :premises (@p459) :args (@t455)) % 175.23/175.52 (step @p461 :rule refl :args (@t436)) % 175.23/175.52 (step @p462 :rule refl :args (@t425)) % 175.23/175.52 (step @p463 :rule nary_cong :premises (@p462 @p461 @p460 @p444) :args (@t456)) % 175.23/175.52 (step @p464 :rule cong :premises (@p463) :args (@t457)) % 175.23/175.52 (step @p465 :rule refl :args (tptp.hoaslaminj)) % 175.23/175.52 (step @p466 :rule cong :premises (@p465 @p464) :args ((= tptp.hoaslaminj @t457))) % 175.23/175.52 (step @p467 :rule refl :args (@t430)) % 175.23/175.52 (step @p468 :rule and_elim :premises (@p1) :args (6)) % 175.23/175.52 (step @p469 :rule and_elim :premises (@p1) :args (11)) % 175.23/175.52 (step @p470 :rule cong :premises (@p469 @p468) :args (@t458)) % 175.23/175.52 (step @p471 :rule cong :premises (@p470) :args (@t459)) % 175.23/175.52 (step @p472 :rule cong :premises (@p469 @p468) :args (@t460)) % 175.23/175.52 (step @p473 :rule cong :premises (@p472) :args (@t461)) % 175.23/175.52 (step @p474 :rule cong :premises (@p473 @p471) :args (@t462)) % 175.23/175.52 (step @p475 :rule cong :premises (@p474) :args (@t463)) % 175.23/175.52 (step @p476 :rule refl :args (@t436)) % 175.23/175.52 (step @p477 :rule nary_cong :premises (@p427 @p476 @p475 @p467) :args (@t464)) % 175.23/175.52 (step @p478 :rule cong :premises (@p477) :args (@t465)) % 175.23/175.52 (step @p479 :rule cong :premises (@p465 @p478) :args ((= tptp.hoaslaminj @t465))) % 175.23/175.52 (step @p480 :rule trans :premises (@p479 @p466)) % 175.23/175.52 (step @p481 :rule refl :args (@t428)) % 175.23/175.52 (step @p482 :rule refl :args (@t110)) % 175.23/175.52 (step @p483 :rule cong :premises (@p482 @p481) :args ((= @t110 @t428))) % 175.23/175.52 (step @p484 :rule symm :premises (@p483)) % 175.23/175.52 (step @p485 :rule eq_resolve :premises (@p482 @p484)) % 175.23/175.52 (step @p486 :rule refl :args (@t429)) % 175.23/175.52 (step @p487 :rule refl :args (@t111)) % 175.23/175.52 (step @p488 :rule cong :premises (@p487 @p486) :args ((= @t111 @t429))) % 175.23/175.52 (step @p489 :rule symm :premises (@p488)) % 175.23/175.52 (step @p490 :rule eq_resolve :premises (@p487 @p489)) % 175.23/175.52 (step @p491 :rule cong :premises (@p490 @p485) :args (@t112)) % 175.23/175.52 (step @p492 :rule refl :args ((tptp.lam @t113))) % 175.23/175.52 (step @p493 :rule refl :args (@t458)) % 175.23/175.52 (step @p494 :rule cong :premises (@p493) :args (@t459)) % 175.23/175.52 (step @p495 :rule trans :premises (@p494 @p492)) % 175.23/175.52 (step @p496 :rule refl :args (tptp.lam)) % 175.23/175.52 (step @p497 :rule ho_cong :premises (@p496 @p493)) % 175.23/175.52 (step @p498 :rule cong :premises (@p497 @p495) :args ((= (_ tptp.lam @t458) @t459))) % 175.23/175.52 (step @p499 :rule symm :premises (@p498)) % 175.23/175.52 (step @p500 :rule refl :args (@t114)) % 175.23/175.52 (step @p501 :rule eq_resolve :premises (@p500 @p499)) % 175.23/175.52 (step @p502 :rule refl :args (@t113)) % 175.23/175.52 (step @p503 :rule cong :premises (@p502 @p493) :args ((= @t113 @t458))) % 175.23/175.52 (step @p504 :rule symm :premises (@p503)) % 175.23/175.52 (step @p505 :rule eq_resolve :premises (@p502 @p504)) % 175.23/175.52 (step @p506 :rule ho_cong :premises (@p496 @p505)) % 175.23/175.52 (step @p507 :rule trans :premises (@p506 @p501)) % 175.23/175.52 (step @p508 :rule refl :args ((tptp.lam @t5))) % 175.23/175.52 (step @p509 :rule refl :args (@t460)) % 175.23/175.52 (step @p510 :rule cong :premises (@p509) :args (@t461)) % 175.23/175.52 (step @p511 :rule trans :premises (@p510 @p508)) % 175.23/175.52 (step @p512 :rule ho_cong :premises (@p496 @p509)) % 175.23/175.52 (step @p513 :rule cong :premises (@p512 @p511) :args ((= (_ tptp.lam @t460) @t461))) % 175.23/175.52 (step @p514 :rule symm :premises (@p513)) % 175.23/175.52 (step @p515 :rule refl :args (@t6)) % 175.23/175.52 (step @p516 :rule eq_resolve :premises (@p515 @p514)) % 175.23/175.52 (step @p517 :rule refl :args (@t5)) % 175.23/175.52 (step @p518 :rule cong :premises (@p517 @p509) :args ((= @t5 @t460))) % 175.23/175.52 (step @p519 :rule symm :premises (@p518)) % 175.23/175.52 (step @p520 :rule eq_resolve :premises (@p517 @p519)) % 175.23/175.52 (step @p521 :rule ho_cong :premises (@p496 @p520)) % 175.23/175.52 (step @p522 :rule trans :premises (@p521 @p516)) % 175.23/175.52 (step @p523 :rule cong :premises (@p522 @p507) :args (@t115)) % 175.23/175.52 (step @p524 :rule cong :premises (@p523) :args (@t116)) % 175.23/175.52 (step @p525 :rule nary_cong :premises (@p462 @p461 @p524 @p491) :args (@t466)) % 175.23/175.52 (step @p526 :rule cong :premises (@p525) :args ((forall @t124 @t466))) % 175.23/175.52 (step @p527 :rule refl :args (@t112)) % 175.23/175.52 (step @p528 :rule refl :args (@t116)) % 175.23/175.52 (step @p529 :rule refl :args ((_ @t109 @t18 @t15))) % 175.23/175.52 (step @p530 :rule refl :args (@t418)) % 175.23/175.52 (step @p531 :rule refl :args (@t419)) % 175.23/175.52 (step @p532 :rule cong :premises (@p531 @p530) :args (@t433)) % 175.23/175.52 (step @p533 :rule trans :premises (@p532 @p529)) % 175.23/175.52 (step @p534 :rule refl :args (@t109)) % 175.23/175.52 (step @p535 :rule ho_cong :premises (@p534 @p531)) % 175.23/175.52 (step @p536 :rule ho_cong :premises (@p535 @p530)) % 175.23/175.52 (step @p537 :rule cong :premises (@p536 @p533) :args ((= (_ (_ @t109 @t419) @t418) @t433))) % 175.23/175.52 (step @p538 :rule symm :premises (@p537)) % 175.23/175.52 (step @p539 :rule refl :args (@t117)) % 175.23/175.52 (step @p540 :rule eq_resolve :premises (@p539 @p538)) % 175.23/175.52 (step @p541 :rule refl :args (@t15)) % 175.23/175.52 (step @p542 :rule cong :premises (@p541 @p530) :args ((= @t15 @t418))) % 175.23/175.52 (step @p543 :rule symm :premises (@p542)) % 175.23/175.52 (step @p544 :rule eq_resolve :premises (@p541 @p543)) % 175.23/175.52 (step @p545 :rule refl :args (@t18)) % 175.23/175.52 (step @p546 :rule cong :premises (@p545 @p531) :args ((= @t18 @t419))) % 175.23/175.52 (step @p547 :rule symm :premises (@p546)) % 175.23/175.52 (step @p548 :rule eq_resolve :premises (@p545 @p547)) % 175.23/175.52 (step @p549 :rule ho_cong :premises (@p534 @p548)) % 175.23/175.52 (step @p550 :rule ho_cong :premises (@p549 @p544)) % 175.23/175.52 (step @p551 :rule trans :premises (@p550 @p540)) % 175.23/175.52 (step @p552 :rule refl :args ((tptp.sub @t118 @t13))) % 175.23/175.52 (step @p553 :rule refl :args (@t13)) % 175.23/175.52 (step @p554 :rule refl :args (@t434)) % 175.23/175.52 (step @p555 :rule cong :premises (@p554 @p553) :args (@t435)) % 175.23/175.52 (step @p556 :rule trans :premises (@p555 @p552)) % 175.23/175.52 (step @p557 :rule refl :args (tptp.sub)) % 175.23/175.52 (step @p558 :rule ho_cong :premises (@p557 @p554)) % 175.23/175.52 (step @p559 :rule ho_cong :premises (@p558 @p553)) % 175.23/175.52 (step @p560 :rule cong :premises (@p559 @p556) :args ((= (_ (_ tptp.sub @t434) @t13) @t435))) % 175.23/175.52 (step @p561 :rule symm :premises (@p560)) % 175.23/175.52 (step @p562 :rule refl :args (@t119)) % 175.23/175.52 (step @p563 :rule eq_resolve :premises (@p562 @p561)) % 175.23/175.52 (step @p564 :rule refl :args (@t118)) % 175.23/175.52 (step @p565 :rule cong :premises (@p564 @p554) :args ((= @t118 @t434))) % 175.23/175.52 (step @p566 :rule symm :premises (@p565)) % 175.23/175.52 (step @p567 :rule eq_resolve :premises (@p564 @p566)) % 175.23/175.52 (step @p568 :rule ho_cong :premises (@p557 @p567)) % 175.23/175.52 (step @p569 :rule ho_cong :premises (@p568 @p553)) % 175.23/175.52 (step @p570 :rule trans :premises (@p569 @p563)) % 175.23/175.52 (step @p571 :rule cong :premises (@p570 @p551) :args (@t120)) % 175.23/175.52 (step @p572 :rule cong :premises (@p571) :args (@t121)) % 175.23/175.52 (step @p573 :rule cong :premises (@p572) :args (@t122)) % 175.23/175.52 (step @p574 :rule refl :args ((_ @t4 @t18 @t15))) % 175.23/175.52 (step @p575 :rule cong :premises (@p531 @p530) :args (@t421)) % 175.23/175.52 (step @p576 :rule trans :premises (@p575 @p574)) % 175.23/175.52 (step @p577 :rule refl :args (@t4)) % 175.23/175.52 (step @p578 :rule ho_cong :premises (@p577 @p531)) % 175.23/175.52 (step @p579 :rule ho_cong :premises (@p578 @p530)) % 175.23/175.52 (step @p580 :rule cong :premises (@p579 @p576) :args ((= (_ (_ @t4 @t419) @t418) @t421))) % 175.23/175.52 (step @p581 :rule symm :premises (@p580)) % 175.23/175.52 (step @p582 :rule refl :args (@t19)) % 175.23/175.52 (step @p583 :rule eq_resolve :premises (@p582 @p581)) % 175.23/175.52 (step @p584 :rule ho_cong :premises (@p577 @p548)) % 175.23/175.52 (step @p585 :rule ho_cong :premises (@p584 @p544)) % 175.23/175.52 (step @p586 :rule trans :premises (@p585 @p583)) % 175.23/175.52 (step @p587 :rule refl :args ((tptp.sub @t20 @t13))) % 175.23/175.52 (step @p588 :rule refl :args (@t422)) % 175.23/175.52 (step @p589 :rule cong :premises (@p588 @p553) :args (@t423)) % 175.23/175.52 (step @p590 :rule trans :premises (@p589 @p587)) % 175.23/175.52 (step @p591 :rule ho_cong :premises (@p557 @p588)) % 175.23/175.52 (step @p592 :rule ho_cong :premises (@p591 @p553)) % 175.23/175.52 (step @p593 :rule cong :premises (@p592 @p590) :args ((= (_ (_ tptp.sub @t422) @t13) @t423))) % 175.23/175.52 (step @p594 :rule symm :premises (@p593)) % 175.23/175.52 (step @p595 :rule refl :args (@t21)) % 175.23/175.52 (step @p596 :rule eq_resolve :premises (@p595 @p594)) % 175.23/175.52 (step @p597 :rule refl :args (@t20)) % 175.23/175.52 (step @p598 :rule cong :premises (@p597 @p588) :args ((= @t20 @t422))) % 175.23/175.52 (step @p599 :rule symm :premises (@p598)) % 175.23/175.52 (step @p600 :rule eq_resolve :premises (@p597 @p599)) % 175.23/175.52 (step @p601 :rule ho_cong :premises (@p557 @p600)) % 175.23/175.52 (step @p602 :rule ho_cong :premises (@p601 @p553)) % 175.23/175.52 (step @p603 :rule trans :premises (@p602 @p596)) % 175.23/175.52 (step @p604 :rule cong :premises (@p603 @p586) :args (@t22)) % 175.23/175.52 (step @p605 :rule cong :premises (@p604) :args (@t24)) % 175.23/175.52 (step @p606 :rule cong :premises (@p605) :args (@t25)) % 175.23/175.52 (step @p607 :rule nary_cong :premises (@p606 @p573 @p528 @p527) :args (@t123)) % 175.23/175.52 (step @p608 :rule cong :premises (@p607) :args (@t125)) % 175.23/175.52 (step @p609 :rule trans :premises (@p608 @p526)) % 175.23/175.52 (step @p610 :rule cong :premises (@p465 @p609) :args (@t156)) % 175.23/175.52 (step @p611 :rule and_elim :premises (@p1) :args (40)) % 175.23/175.52 (step @p612 :rule eq_resolve :premises (@p611 @p610)) % 175.23/175.52 (step @p613 :rule eq_resolve :premises (@p612 @p480)) % 175.23/175.52 (step @p614 :rule cong :premises (@p613 @p443) :args (@t467)) % 175.23/175.52 (step @p615 :rule cong :premises (@p614) :args ((not @t467))) % 175.23/175.52 (step @p616 :rule trans :premises (@p615 @p433)) % 175.23/175.52 (step @p617 :rule aci_norm :args ((= @t469 @t448))) % 175.23/175.52 (step @p618 :rule cong :premises (@p617) :args (@t470)) % 175.23/175.52 (step @p619 :rule quant-merge-prenex :args ((= (forall @t26 @t472) @t470))) % 175.23/175.52 (step @p620 :rule alpha_equiv :args (@t473 (@list @t416 @t275 @t274) (@list @t182 @t475 @t474))) % 175.23/175.52 (step @p621 :rule nary_cong :premises (@p462 @p620) :args (@t476)) % 175.23/175.52 (step @p622 :rule quant-miniscope-or :args ((= @t472 @t476))) % 175.23/175.52 (step @p623 :rule trans :premises (@p622 @p621)) % 175.23/175.52 (step @p624 :rule symm :premises (@p623)) % 175.23/175.52 (step @p625 :rule cong :premises (@p624) :args ((forall @t26 (or @t425 @t485)))) % 175.23/175.52 (step @p626 :rule trans :premises (@p625 @p619)) % 175.23/175.52 (step @p627 :rule trans :premises (@p626 @p618)) % 175.23/175.52 (step @p628 :rule bool-impl-elim :args (@t424 @t485)) % 175.23/175.52 (step @p629 :rule cong :premises (@p628) :args ((forall @t26 (=> @t424 @t485)))) % 175.23/175.52 (step @p630 :rule trans :premises (@p629 @p627)) % 175.23/175.52 (step @p631 :rule quant-merge-prenex :args ((= (forall @t199 @t487) @t485))) % 175.23/175.52 (step @p632 :rule alpha_equiv :args (@t488 (@list @t475 @t474) (@list @t16 @t8))) % 175.23/175.52 (step @p633 :rule refl :args (@t478)) % 175.23/175.52 (step @p634 :rule refl :args (@t483)) % 175.23/175.52 (step @p635 :rule nary_cong :premises (@p634 @p633 @p632) :args (@t489)) % 175.23/175.52 (step @p636 :rule quant-miniscope-or :args ((= @t487 @t489))) % 175.23/175.52 (step @p637 :rule trans :premises (@p636 @p635)) % 175.23/175.52 (step @p638 :rule symm :premises (@p637)) % 175.23/175.52 (step @p639 :rule cong :premises (@p638) :args ((forall @t199 (or @t483 @t478 @t490)))) % 175.23/175.52 (step @p640 :rule trans :premises (@p639 @p631)) % 175.23/175.52 (step @p641 :rule refl :args (@t490)) % 175.23/175.52 (step @p642 :rule lambda-elim :args ((= @t491 @t182))) % 175.23/175.52 (step @p643 :rule refl :args (tptp.id)) % 175.23/175.52 (step @p644 :rule cong :premises (@p643 @p642) :args (@t492)) % 175.23/175.52 (step @p645 :rule lambda-elim :args ((= @t493 @t4))) % 175.23/175.52 (step @p646 :rule cong :premises (@p643 @p645) :args (@t494)) % 175.23/175.52 (step @p647 :rule cong :premises (@p646 @p644) :args (@t495)) % 175.23/175.52 (step @p648 :rule cong :premises (@p647) :args (@t496)) % 175.23/175.52 (step @p649 :rule refl :args (@t483)) % 175.23/175.52 (step @p650 :rule nary_cong :premises (@p649 @p648 @p641) :args (@t497)) % 175.23/175.52 (step @p651 :rule cong :premises (@p650) :args ((forall @t199 @t497))) % 175.23/175.52 (step @p652 :rule trans :premises (@p651 @p640)) % 175.23/175.52 (step @p653 :rule refl :args (@t490)) % 175.23/175.52 (step @p654 :rule refl :args ((tptp.hoaslam tptp.id @t187))) % 175.23/175.52 (step @p655 :rule refl :args (@t480)) % 175.23/175.52 (step @p656 :rule cong :premises (@p655) :args (@t491)) % 175.23/175.52 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(step-pop @p1068 :rule scope :premises (@p1067)) % 175.23/175.52 (step-pop @p1069 :rule scope :premises (@p1068)) % 175.23/175.52 (step-pop @p1070 :rule scope :premises (@p1069)) % 175.23/175.52 (step-pop @p1071 :rule scope :premises (@p1070)) % 175.23/175.52 (step-pop @p1072 :rule scope :premises (@p1071)) % 175.23/175.52 (step @p882 :rule process_scope :premises (@p1072) :args (@t537)) % 175.23/175.52 (step @p890 :rule and_intro :premises (@p110 @p115 @p13 @p143 @p144 @p8 @p1034)) % 175.23/175.52 (step @p891 :rule modus_ponens :premises (@p890 @p882)) % 175.23/175.52 (step @p892 :rule and_intro :premises (@p891 @p846 @p845 @p844 @p843 @p842)) % 175.23/175.52 (step @p893 :rule modus_ponens :premises (@p892 @p835)) % 175.23/175.52 (step-pop @p1073 :rule scope :premises (@p893)) % 175.23/175.52 (step-pop @p1074 :rule scope :premises (@p1073)) % 175.23/175.52 (step-pop @p1075 :rule scope :premises (@p1074)) % 175.23/175.52 (step-pop @p1076 :rule scope :premises (@p1075)) % 175.23/175.52 (step-pop @p1077 :rule scope :premises (@p1076)) % 175.23/175.52 (step-pop @p1078 :rule scope :premises (@p1077)) % 175.23/175.52 (step-pop @p1079 :rule scope :premises (@p1078)) % 175.23/175.52 (step-pop @p1080 :rule scope :premises (@p1079)) % 175.23/175.52 (step-pop @p1081 :rule scope :premises (@p1080)) % 175.23/175.52 (step-pop @p1082 :rule scope :premises (@p1081)) % 175.23/175.52 (step-pop @p1083 :rule scope :premises (@p1082)) % 175.23/175.52 (step-pop @p1084 :rule scope :premises (@p1083)) % 175.23/175.52 (step-pop @p1085 :rule scope :premises (@p1084)) % 175.23/175.52 (step-pop @p1086 :rule scope :premises (@p1085)) % 175.23/175.52 (step-pop @p1087 :rule scope :premises (@p1086)) % 175.23/175.52 (step-pop @p1088 :rule scope :premises (@p1087)) % 175.23/175.52 (step-pop @p1089 :rule scope :premises (@p1088)) % 175.23/175.52 (step @p894 :rule process_scope :premises (@p1089) :args (@t512)) % 175.23/175.52 (step @p912 :rule implies_elim :premises (@p894)) % 175.23/175.52 (step @p913 :rule cnf_and_neg :args (@t542)) % 175.23/175.52 (step @p914 :rule resolution :premises (@p913 @p912) :args (true @t542)) % 175.23/175.52 (step @p915 :rule eq_resolve :premises (@p914 @p771)) % 175.23/175.52 (step @p916 :rule reordering :premises (@p915) :args ((or @t535 @t534 @t533 @t532 @t505 @t530 @t529 @t527 @t526 @t524 @t523 @t521 @t520 @t518 @t517 @t512 @t515 @t514))) % 175.23/175.52 (step @p917 :rule chain_m_resolution :premises (@p916 @p8 @p13 @p370 @p340 @p752 @p231 @p203 @p59 @p64 @p110 @p115 @p202 @p174 @p143 @p144 @p173 @p145) :args (@t512 (@list false false false false true false false false false false false false false false false false false) (@list @t215 @t220 @t394 @t531 @t505 @t348 @t528 @t263 @t525 @t292 @t522 @t331 @t519 @t303 @t516 @t315 @t513))) % 175.23/175.52 (step @p918 :rule eq-symm :args (@t504 @t221)) % 175.23/175.52 (step @p919 :rule cong :premises (@p918) :args (@t543)) % 175.23/175.52 (step @p920 :rule cong :premises (@p919) :args (@t544)) % 175.23/175.52 (step @p921 :rule cong :premises (@p920) :args (@t545)) % 175.23/175.52 (step @p922 :rule cong :premises (@p35 @p921) :args ((=> @t222 @t545))) % 175.23/175.53 (assume-push @p1090 @t222) % 175.23/175.53 (step @p924 :rule instantiate :premises (@p30) :args ((@list @t504))) % 175.23/175.53 (step-pop @p1091 :rule scope :premises (@p924)) % 175.23/175.53 (step @p925 :rule process_scope :premises (@p1091) :args (@t545)) % 175.23/175.53 (step @p927 :rule eq_resolve :premises (@p925 @p922)) % 175.23/175.53 (step @p928 :rule implies_elim :premises (@p927)) % 175.23/175.53 (step @p929 :rule chain_m_resolution :premises (@p928 @p30) :args (@t547 @t259 @t260)) % 175.23/175.53 (step @p930 :rule refl :args (@t550)) % 175.23/175.53 (step @p931 :rule bool-double-not-elim :args (@t546)) % 175.23/175.53 (step @p932 :rule nary_cong :premises (@p931 @p930) :args ((or (not @t547) @t550))) % 175.23/175.53 (step @p933 :rule eq-symm :args (@t549 @t504)) % 175.23/175.53 (step @p934 :rule bool-double-not-elim :args (@t551)) % 175.23/175.53 (step @p935 :rule trans :premises (@p934 @p933)) % 175.23/175.53 (step @p936 :rule refl :args (@t547)) % 175.23/175.53 (step @p937 :rule cong :premises (@p936 @p935) :args ((=> @t547 @t552))) % 175.23/175.53 (assume-push @p1092 @t547) % 175.23/175.53 (step @p939 :rule skolemize :premises (@p929)) % 175.23/175.53 (step-pop @p1093 :rule scope :premises (@p939)) % 175.23/175.53 (step @p940 :rule process_scope :premises (@p1093) :args (@t552)) % 175.23/175.53 (step @p942 :rule eq_resolve :premises (@p940 @p937)) % 175.23/175.53 (step @p943 :rule implies_elim :premises (@p942)) % 175.23/175.53 (step @p944 :rule eq_resolve :premises (@p943 @p932)) % 175.23/175.53 (step @p945 :rule chain_m_resolution :premises (@p944 @p929) :args (@t550 @t266 (@list @t546))) % 175.23/175.53 (step @p946 :rule instantiate :premises (@p63) :args ((@list @t548))) % 175.23/175.53 (assume-push @p1094 @t215) % 175.23/175.53 (assume-push @p1095 @t220) % 175.23/175.53 (assume-push @p1096 @t263) % 175.23/175.53 (assume-push @p1097 @t525) % 175.23/175.53 (assume-push @p1098 @t292) % 175.23/175.53 (assume-push @p1099 @t522) % 175.23/175.53 (assume-push @p1100 @t303) % 175.23/175.53 (assume-push @p1101 @t516) % 175.23/175.53 (assume-push @p1102 @t550) % 175.23/175.53 (assume-push @p1103 @t553) % 175.23/175.53 (step @p867 :rule refl :args (@t502)) % 175.23/175.53 (step @p873 :rule cong :premises (@p867 @p265) :args (@t540)) % 175.23/175.53 (step @p957 :rule cong :premises (@p873 @p304) :args (@t541)) % 175.23/175.53 (step @p958 :rule symm :premises (@p144)) % 175.23/175.53 (step @p959 :rule cong :premises (@p302 @p958) :args (@t302)) % 175.23/175.53 (step @p960 :rule trans :premises (@p143 @p959 @p8)) % 175.23/175.53 (step @p875 :rule symm :premises (@p873)) % 175.23/175.53 (step @p961 :rule cong :premises (@p875 @p960) :args (@t539)) % 175.23/175.53 (step @p863 :rule refl :args (@t295)) % 175.23/175.53 (step @p962 :rule symm :premises (@p115)) % 175.23/175.53 (step @p963 :rule cong :premises (@p263 @p962) :args (@t291)) % 175.23/175.53 (step @p964 :rule trans :premises (@p110 @p963)) % 175.23/175.53 (step @p965 :rule cong :premises (@p867 @p964) :args (@t503)) % 175.23/175.53 (step @p966 :rule cong :premises (@p965 @p863) :args (@t504)) % 175.23/175.53 (step @p967 :rule symm :premises (@p945)) % 175.23/175.53 (step @p968 :rule cong :premises (@p302 @p946) :args (@t210)) % 175.23/175.53 (step @p806 :rule symm :premises (@p64)) % 175.23/175.53 (step @p807 :rule cong :premises (@p302 @p806) :args (@t262)) % 175.23/175.53 (step @p969 :rule trans :premises (@p59 @p807 @p968 @p967 @p966 @p961 @p957)) % 175.23/175.53 (step-pop @p1104 :rule scope :premises (@p969)) % 175.23/175.53 (step-pop @p1105 :rule scope :premises (@p1104)) % 175.23/175.53 (step-pop @p1106 :rule scope :premises (@p1105)) % 175.23/175.53 (step-pop @p1107 :rule scope :premises (@p1106)) % 175.23/175.53 (step-pop @p1108 :rule scope :premises (@p1107)) % 175.23/175.53 (step-pop @p1109 :rule scope :premises (@p1108)) % 175.23/175.53 (step-pop @p1110 :rule scope :premises (@p1109)) % 175.23/175.53 (step-pop @p1111 :rule scope :premises (@p1110)) % 175.23/175.53 (step-pop @p1112 :rule scope :premises (@p1111)) % 175.23/175.53 (step-pop @p1113 :rule scope :premises (@p1112)) % 175.23/175.53 (step @p970 :rule process_scope :premises (@p1113) :args (@t511)) % 175.23/175.53 (step @p981 :rule implies_elim :premises (@p970)) % 175.23/175.53 (step @p982 :rule cnf_and_neg :args (@t554)) % 175.23/175.53 (step @p983 :rule resolution :premises (@p982 @p981) :args (true @t554)) % 175.23/175.53 (step @p984 :rule reordering :premises (@p983) :args ((or @t535 @t534 @t527 @t526 @t524 @t523 @t518 @t517 @t511 (not @t550) (not @t553)))) % 175.23/175.53 (step @p985 false :rule chain_m_resolution :premises (@p984 @p946 @p945 @p917 @p144 @p143 @p115 @p110 @p64 @p59 @p13 @p8) :args (false (@list false false true false false false false false false false false) (@list @t553 @t550 @t511 @t516 @t303 @t522 @t292 @t525 @t263 @t220 @t215))) % 175.23/175.53 ) % 175.23/175.53 % SZS output end Proof % 175.23/175.53 % cvc5 exiting %------------------------------------------------------------------------------