%------------------------------------------------------------------------------ % 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 : n009.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 09:07:16 AM UTC 2026 % Result : Theorem 170.30s 170.64s % Output : Proof 170.30s % 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 % 0.17/0.34 % Computer : n009.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 23:02:14 EDT 2026 % 0.17/0.34 % CPUTime : % 0.36/0.56 %----Proving TH0 % 170.30/170.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 170.30/170.64 --- 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... % 170.30/170.64 --- 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... % 170.30/170.64 --- Run --ho-elim --full-saturate-quant at 18s... % 170.30/170.64 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 170.30/170.64 % SZS status Theorem % 170.30/170.64 % SZS output start Proof % 170.30/170.64 ( % 170.30/170.64 (declare-sort tptp.term 0) % 170.30/170.64 (declare-sort tptp.subst 0) % 170.30/170.64 (declare-sort tptp.d_term 0) % 170.30/170.64 (declare-sort tptp.d_subst 0) % 170.30/170.64 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 170.30/170.64 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 170.30/170.64 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 170.30/170.64 (declare-const tptp.pushprop_lem1v2 Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem1_gthm Bool) % 170.30/170.64 (declare-const tptp.axmap Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem0_gthm Bool) % 170.30/170.64 (declare-const tptp.shinj Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem1v2 Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 170.30/170.64 (declare-const tptp.induction2lem Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 170.30/170.64 (declare-const tptp.axvarshift Bool) % 170.30/170.64 (declare-const tptp.hoasapinj2 Bool) % 170.30/170.64 (declare-const tptp.hoasapnotvar_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasapinj1 Bool) % 170.30/170.64 (declare-const tptp.ulamvar1 Bool) % 170.30/170.64 (declare-const tptp.induction2lem_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 170.30/170.64 (declare-const tptp.apnotvar Bool) % 170.30/170.64 (declare-const tptp.pushprop_lthm_orig Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 170.30/170.64 (declare-const tptp.hoaslaminj Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3aaa Bool) % 170.30/170.64 (declare-const tptp.induction2lem_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3 Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem2 Bool) % 170.30/170.64 (declare-const tptp.termmset_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem1 Bool) % 170.30/170.64 (declare-const tptp.hoaslamnotap_lthm Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasapnotvar Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem0 Bool) % 170.30/170.64 (declare-const tptp.hoasinduction Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_gthm Bool) % 170.30/170.64 (declare-const tptp.axapp Bool) % 170.30/170.64 (declare-const tptp.hoaslamnotvar_lthm Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 170.30/170.64 (declare-const tptp.ulamvarind Bool) % 170.30/170.64 (declare-const tptp.induction Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 170.30/170.64 (declare-const tptp.termmset_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3aa Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 170.30/170.64 (declare-const tptp.hoaslamnotap_gthm Bool) % 170.30/170.64 (declare-const tptp.hoaslamnotvar_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem2v2 Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 170.30/170.64 (declare-const tptp.axclos Bool) % 170.30/170.64 (declare-const tptp.axassoc Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem2v2 Bool) % 170.30/170.64 (declare-const tptp.pushprop_lthm Bool) % 170.30/170.64 (declare-const tptp.apinj2 Bool) % 170.30/170.64 (declare-const tptp.apinj1 Bool) % 170.30/170.64 (declare-const tptp.hoasapinj2_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3v2a Bool) % 170.30/170.64 (declare-const tptp.hoasapinj1_lthm Bool) % 170.30/170.64 (declare-const tptp.hoaslaminj_lthm Bool) % 170.30/170.64 (declare-const tptp.axvarcons Bool) % 170.30/170.64 (declare-const tptp.axscons Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 170.30/170.64 (declare-const tptp.d_one tptp.d_term) % 170.30/170.64 (declare-const tptp.hoaslamnotap Bool) % 170.30/170.64 (declare-const tptp.ulamvarsh Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem3v2 Bool) % 170.30/170.64 (declare-const tptp.axshiftcons Bool) % 170.30/170.64 (declare-const tptp.id tptp.subst) % 170.30/170.64 (declare-const tptp.pushprop_lem1_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 170.30/170.64 (declare-const tptp.pushprop_lem0_lthm Bool) % 170.30/170.64 (declare-const tptp.one tptp.term) % 170.30/170.64 (declare-const tptp.substmonoid_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3v2 Bool) % 170.30/170.64 (declare-const tptp.sh tptp.subst) % 170.30/170.64 (declare-const tptp.termmset Bool) % 170.30/170.64 (declare-const tptp.induction2 Bool) % 170.30/170.64 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 170.30/170.64 (declare-const tptp.lam (-> tptp.term tptp.term)) % 170.30/170.64 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 170.30/170.64 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 170.30/170.64 (declare-const tptp.axvarid Bool) % 170.30/170.64 (declare-const tptp.d_id tptp.d_subst) % 170.30/170.64 (declare-const tptp.var (-> tptp.term Bool)) % 170.30/170.64 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 170.30/170.64 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 170.30/170.64 (declare-const tptp.hoasapnotvar_lthm Bool) % 170.30/170.64 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 170.30/170.64 (declare-const tptp.hoasinduction_lthm_3 Bool) % 170.30/170.64 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 170.30/170.64 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 170.30/170.64 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 170.30/170.64 (declare-const tptp.induction2_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3a Bool) % 170.30/170.64 (declare-const tptp.lamnotvar Bool) % 170.30/170.64 (declare-const tptp.substmonoid Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3b Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 170.30/170.64 (declare-const tptp.pushprop Bool) % 170.30/170.64 (declare-const tptp.substmonoid_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 170.30/170.64 (declare-const tptp.induction2_lthm Bool) % 170.30/170.64 (declare-const tptp.hoaslaminj_gthm Bool) % 170.30/170.64 (declare-const tptp.axidl Bool) % 170.30/170.64 (declare-const tptp.hoaslamnotvar Bool) % 170.30/170.64 (declare-const tptp.hoasapinj1_gthm Bool) % 170.30/170.64 (declare-const tptp.lamnotap Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasapinj2_gthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 170.30/170.64 (declare-const tptp.axabs Bool) % 170.30/170.64 (declare-const tptp.pushprop_gthm Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem0 Bool) % 170.30/170.64 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 170.30/170.64 (declare-const tptp.laminj Bool) % 170.30/170.64 (declare-const tptp.pushprop_lem1 Bool) % 170.30/170.64 (declare-const tptp.axidr Bool) % 170.30/170.64 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 170.30/170.64 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 170.30/170.64 (define @t3 () (_ @t2 tptp.id)) % 170.30/170.64 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 170.30/170.64 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 170.30/170.64 (define @t6 () (_ tptp.lam @t5)) % 170.30/170.64 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 170.30/170.64 (define @t8 () (@var "A" tptp.term)) % 170.30/170.64 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 170.30/170.64 (define @t10 () (not @t9)) % 170.30/170.64 (define @t11 () (@list @t8)) % 170.30/170.64 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 170.30/170.64 (define @t13 () (@var "N" tptp.subst)) % 170.30/170.64 (define @t14 () (_ tptp.sub @t8)) % 170.30/170.64 (define @t15 () (_ @t14 @t13)) % 170.30/170.64 (define @t16 () (@var "M" tptp.subst)) % 170.30/170.64 (define @t17 () (_ tptp.comp @t16)) % 170.30/170.64 (define @t18 () (_ @t17 @t13)) % 170.30/170.64 (define @t19 () (_ (_ @t4 @t16) @t8)) % 170.30/170.64 (define @t20 () (@list @t16 @t8 @t13)) % 170.30/170.64 (define @t21 () (not (forall @t20 (= (_ (_ tptp.sub @t19) @t13) (_ (_ @t4 @t18) @t15))))) % 170.30/170.64 (define @t22 () (@list @t4)) % 170.30/170.64 (define @t23 () (not (forall @t22 (or @t21 @t12 @t7)))) % 170.30/170.64 (define @t24 () (@var "B" tptp.term)) % 170.30/170.64 (define @t25 () (_ @t14 tptp.id)) % 170.30/170.64 (define @t26 () (_ tptp.ap @t25)) % 170.30/170.64 (define @t27 () (_ @t26 @t24)) % 170.30/170.64 (define @t28 () (_ (_ @t3 @t27) tptp.id)) % 170.30/170.64 (define @t29 () (_ (_ @t3 @t24) tptp.id)) % 170.30/170.64 (define @t30 () (not @t29)) % 170.30/170.64 (define @t31 () (or @t10 @t30 @t28)) % 170.30/170.64 (define @t32 () (@list @t8 @t24)) % 170.30/170.64 (define @t33 () (forall @t32 @t31)) % 170.30/170.64 (define @t34 () (not @t33)) % 170.30/170.64 (define @t35 () (@var "K" tptp.subst)) % 170.30/170.64 (define @t36 () (_ (_ tptp.comp @t35) @t13)) % 170.30/170.64 (define @t37 () (_ (_ @t2 @t16) @t8)) % 170.30/170.64 (define @t38 () (_ @t37 @t36)) % 170.30/170.64 (define @t39 () (_ @t14 @t35)) % 170.30/170.64 (define @t40 () (_ @t17 @t35)) % 170.30/170.64 (define @t41 () (_ (_ (_ @t2 @t40) @t39) @t13)) % 170.30/170.64 (define @t42 () (not @t41)) % 170.30/170.64 (define @t43 () (or @t42 @t38)) % 170.30/170.64 (define @t44 () (@list @t16 @t8 @t13 @t35)) % 170.30/170.64 (define @t45 () (forall @t44 @t43)) % 170.30/170.64 (define @t46 () (not @t45)) % 170.30/170.64 (define @t47 () (not @t38)) % 170.30/170.64 (define @t48 () (or @t47 @t41)) % 170.30/170.64 (define @t49 () (forall @t44 @t48)) % 170.30/170.64 (define @t50 () (not @t49)) % 170.30/170.64 (define @t51 () (forall (@list @t2 @t1) (or @t50 @t46 (not (forall @t11 (or (not (_ tptp.var @t25)) @t9))) @t34 @t23 (_ (_ @t3 @t1) tptp.id)))) % 170.30/170.64 (define @t52 () (@var "Bound_variable_2931" tptp.term)) % 170.30/170.64 (define @t53 () (@var "Q" (-> tptp.term Bool))) % 170.30/170.64 (define @t54 () (_ tptp.push @t24)) % 170.30/170.64 (define @t55 () (_ @t54 tptp.id)) % 170.30/170.64 (define @t56 () (not (_ @t53 @t24))) % 170.30/170.64 (define @t57 () (@list @t24)) % 170.30/170.64 (define @t58 () (@var "X" tptp.term)) % 170.30/170.64 (define @t59 () (_ @t53 @t58)) % 170.30/170.64 (define @t60 () (@list @t58)) % 170.30/170.64 (define @t61 () (forall @t60 (= @t59 (_ (_ @t3 @t58) tptp.id)))) % 170.30/170.64 (define @t62 () (not @t61)) % 170.30/170.64 (define @t63 () (forall (@list @t2 @t53 @t52) (or @t23 @t62 (not (forall @t57 (or @t56 (_ @t53 (_ (_ tptp.sub @t52) @t55))))) (_ @t53 (_ tptp.lam @t52))))) % 170.30/170.64 (define @t64 () (forall @t11 (= @t8 @t25))) % 170.30/170.64 (define @t65 () (@var "Bound_variable_2367" tptp.term)) % 170.30/170.64 (define @t66 () (@var "P" (-> tptp.term Bool))) % 170.30/170.64 (define @t67 () (_ tptp.lam @t8)) % 170.30/170.64 (define @t68 () (_ @t66 @t67)) % 170.30/170.64 (define @t69 () (not (_ @t66 @t24))) % 170.30/170.64 (define @t70 () (not (forall @t11 (or (not (forall @t57 (or @t69 (_ @t66 (_ @t14 @t55))))) @t68)))) % 170.30/170.64 (define @t71 () (_ tptp.ap @t8)) % 170.30/170.64 (define @t72 () (_ @t71 @t24)) % 170.30/170.64 (define @t73 () (_ @t66 @t8)) % 170.30/170.64 (define @t74 () (not @t73)) % 170.30/170.64 (define @t75 () (not (forall @t32 (or @t74 @t69 (_ @t66 @t72))))) % 170.30/170.64 (define @t76 () (not (forall @t11 (or (not (_ tptp.var @t8)) @t73)))) % 170.30/170.64 (define @t77 () (forall (@list @t66 @t65) (or @t76 @t75 @t70 (_ @t66 @t65)))) % 170.30/170.64 (define @t78 () (@list @t53)) % 170.30/170.64 (define @t79 () (@list @t2)) % 170.30/170.64 (define @t80 () (forall @t79 (not (forall @t78 @t62)))) % 170.30/170.64 (define @t81 () (@var "Bound_variable_2910" tptp.term)) % 170.30/170.64 (define @t82 () (forall (@list @t2 @t53 @t81) (or @t50 @t46 @t23 @t62 (not (forall @t57 (or @t56 (_ @t53 (_ (_ tptp.sub @t81) @t55))))) (_ @t53 (_ tptp.lam @t81))))) % 170.30/170.64 (define @t83 () (_ (_ tptp.push @t8) @t16)) % 170.30/170.64 (define @t84 () (forall @t60 (= @t59 (_ @t66 (_ (_ tptp.sub @t58) @t83))))) % 170.30/170.64 (define @t85 () (not @t84)) % 170.30/170.64 (define @t86 () (forall (@list @t66 @t8 @t16) (not (forall @t78 @t85)))) % 170.30/170.64 (define @t87 () (_ tptp.comp tptp.sh)) % 170.30/170.64 (define @t88 () (@list @t8 @t16)) % 170.30/170.64 (define @t89 () (forall @t88 (= @t16 (_ @t87 @t83)))) % 170.30/170.64 (define @t90 () (@var "K" (-> tptp.term Bool))) % 170.30/170.64 (define @t91 () (forall (@list @t66 @t90 @t8 @t16 @t24) (or @t74 (_ @t90 (_ @t14 (_ @t54 @t16)))))) % 170.30/170.64 (define @t92 () (_ tptp.sub tptp.one)) % 170.30/170.64 (define @t93 () (forall @t88 (= @t8 (_ @t92 @t83)))) % 170.30/170.64 (define @t94 () (@var "Bound_variable_2605" tptp.term)) % 170.30/170.64 (define @t95 () (@var "Bound_variable_2603" tptp.term)) % 170.30/170.64 (define @t96 () (_ tptp.d2subst tptp.d_id)) % 170.30/170.64 (define @t97 () (_ tptp.d2term tptp.d_one)) % 170.30/170.64 (define @t98 () (@var "Bound_variable_3295" tptp.term)) % 170.30/170.64 (define @t99 () (forall (@list @t2 @t98) (or @t34 @t23 (_ (_ @t3 @t98) tptp.id)))) % 170.30/170.64 (define @t100 () (@var "Bound_variable_3232" tptp.term)) % 170.30/170.64 (define @t101 () (forall (@list @t2 @t100) (or @t23 (not (forall @t57 (or @t30 (_ (_ @t3 (_ (_ tptp.sub @t100) @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t100)) tptp.id)))) % 170.30/170.64 (define @t102 () (@list @t16)) % 170.30/170.64 (define @t103 () (forall @t102 (= @t16 (_ @t17 tptp.id)))) % 170.30/170.64 (define @t104 () (forall @t102 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 170.30/170.64 (define @t105 () (and @t104 @t103)) % 170.30/170.64 (define @t106 () (_ (_ tptp.push tptp.one) tptp.sh)) % 170.30/170.64 (define @t107 () (_ tptp.sub @t24)) % 170.30/170.64 (define @t108 () (forall @t57 (not (forall @t22 (not (= @t5 (_ @t107 @t106))))))) % 170.30/170.64 (define @t109 () (@var "Bound_variable_2342" tptp.subst)) % 170.30/170.64 (define @t110 () (@var "Bound_variable_2340" tptp.term)) % 170.30/170.64 (define @t111 () (forall (@list @t66 @t110 @t109) (or @t75 @t70 (not (forall @t57 (or (not (_ tptp.var @t24)) (_ @t66 (_ @t107 @t109))))) (_ @t66 (_ (_ tptp.sub @t110) @t109))))) % 170.30/170.64 (define @t112 () (forall @t57 (not (forall @t22 (not (forall @t88 (= (_ @t107 @t83) @t19))))))) % 170.30/170.64 (define @t113 () (@var "Bound_variable_3211" tptp.term)) % 170.30/170.64 (define @t114 () (forall (@list @t2 @t113) (or @t50 @t46 @t23 (not (forall @t57 (or @t30 (_ (_ @t3 (_ (_ tptp.sub @t113) @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t113)) tptp.id)))) % 170.30/170.64 (define @t115 () (@var "Bound_variable_3046" tptp.term)) % 170.30/170.64 (define @t116 () (_ tptp.sub @t115)) % 170.30/170.64 (define @t117 () (forall (@list @t2 @t115) (or @t23 (not (forall @t57 (or @t30 (_ (_ @t3 (_ @t116 @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t116 @t106))) tptp.id)))) % 170.30/170.64 (define @t118 () (= @t8 @t24)) % 170.30/170.64 (define @t119 () (forall @t32 (or (not (= @t67 (_ tptp.lam @t24))) @t118))) % 170.30/170.64 (define @t120 () (@var "Bound_variable_2551" tptp.term)) % 170.30/170.64 (define @t121 () (@var "Bound_variable_2549" tptp.subst)) % 170.30/170.64 (define @t122 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 170.30/170.64 (define @t123 () (forall (@list @t4 @t122 @t121 @t120) (or @t21 (not (forall @t20 (= (_ (_ tptp.sub (_ (_ @t122 @t16) @t8)) @t13) (_ (_ @t122 @t18) @t15)))) (not (= @t6 (_ tptp.lam (_ (_ @t122 tptp.sh) tptp.one)))) (= (_ (_ @t4 @t121) @t120) (_ (_ @t122 @t121) @t120))))) % 170.30/170.64 (define @t124 () (@var "D" tptp.term)) % 170.30/170.64 (define @t125 () (@var "C" tptp.term)) % 170.30/170.64 (define @t126 () (not (= (_ @t26 @t125) (_ (_ tptp.ap (_ @t107 tptp.id)) @t124)))) % 170.30/170.64 (define @t127 () (@list @t8 @t24 @t125 @t124)) % 170.30/170.64 (define @t128 () (forall @t127 (or @t126 @t118))) % 170.30/170.64 (define @t129 () (not (= (_ @t71 @t125) (_ (_ tptp.ap @t24) @t124)))) % 170.30/170.64 (define @t130 () (forall @t127 (or @t129 @t118))) % 170.30/170.64 (define @t131 () (= @t125 @t124)) % 170.30/170.64 (define @t132 () (forall @t127 (or @t126 @t131))) % 170.30/170.64 (define @t133 () (forall @t127 (or @t129 @t131))) % 170.30/170.64 (define @t134 () (@var "Bound_variable_2822" tptp.term)) % 170.30/170.64 (define @t135 () (@var "Bound_variable_2820" tptp.term)) % 170.30/170.64 (define @t136 () (@var "Bound_variable_2140" tptp.term)) % 170.30/170.64 (define @t137 () (forall (@list @t66 @t136) (or @t76 @t75 (not (forall @t11 (or @t74 @t68))) (_ @t66 @t136)))) % 170.30/170.64 (define @t138 () (forall (@list @t66 @t53 @t8 @t16) (or @t74 @t85 (_ @t53 tptp.one)))) % 170.30/170.64 (define @t139 () (@var "Bound_variable_3001" tptp.term)) % 170.30/170.64 (define @t140 () (@var "Bound_variable_2999" tptp.term)) % 170.30/170.64 (define @t141 () (_ (_ tptp.ap @t140) @t139)) % 170.30/170.64 (define @t142 () (_ (_ @t3 @t141) tptp.id)) % 170.30/170.64 (define @t143 () (_ (_ @t3 @t139) tptp.id)) % 170.30/170.64 (define @t144 () (not @t143)) % 170.30/170.64 (define @t145 () (_ (_ @t3 @t140) tptp.id)) % 170.30/170.64 (define @t146 () (not @t145)) % 170.30/170.64 (define @t147 () (or @t50 @t46 @t34 @t146 @t144 @t142)) % 170.30/170.64 (define @t148 () (@list @t2 @t140 @t139)) % 170.30/170.64 (define @t149 () (forall @t148 @t147)) % 170.30/170.64 (define @t150 () (= tptp.hoasinduction_lem2 @t149)) % 170.30/170.64 (define @t151 () (@var "Bound_variable_3171" tptp.term)) % 170.30/170.64 (define @t152 () (_ tptp.sub @t151)) % 170.30/170.64 (define @t153 () (@var "Bound_variable_3094" tptp.subst)) % 170.30/170.64 (define @t154 () (@var "Bound_variable_3090" tptp.subst)) % 170.30/170.64 (define @t155 () (_ (_ tptp.comp @t154) @t153)) % 170.30/170.64 (define @t156 () (@var "Bound_variable_3092" tptp.term)) % 170.30/170.64 (define @t157 () (_ (_ tptp.sub @t156) @t153)) % 170.30/170.64 (define @t158 () (@var "Bound_variable_3149" tptp.term)) % 170.30/170.64 (define @t159 () (_ tptp.sub @t158)) % 170.30/170.64 (define @t160 () (@var "Bound_variable_3076" tptp.subst)) % 170.30/170.64 (define @t161 () (@var "Bound_variable_3072" tptp.subst)) % 170.30/170.64 (define @t162 () (@var "Bound_variable_3074" tptp.term)) % 170.30/170.64 (define @t163 () (_ (_ (_ (_ tptp.hoasap @t96) @t97) @t96) @t97)) % 170.30/170.64 (define @t164 () (_ (_ tptp.sub @t97) @t96)) % 170.30/170.64 (define @t165 () (_ (_ tptp.ap @t97) @t97)) % 170.30/170.64 (define @t166 () (@var "DS2" tptp.d_subst)) % 170.30/170.64 (define @t167 () (@var "DS1" tptp.d_subst)) % 170.30/170.64 (define @t168 () (@var "DS" tptp.d_subst)) % 170.30/170.64 (define @t169 () (@list @t168)) % 170.30/170.64 (define @t170 () (@var "S" tptp.subst)) % 170.30/170.64 (define @t171 () (@var "DT2" tptp.d_term)) % 170.30/170.64 (define @t172 () (@var "DT1" tptp.d_term)) % 170.30/170.64 (define @t173 () (@var "DT" tptp.d_term)) % 170.30/170.64 (define @t174 () (@list @t173)) % 170.30/170.64 (define @t175 () (forall @t174 (= @t173 tptp.d_one))) % 170.30/170.64 (define @t176 () (_ tptp.d2term @t173)) % 170.30/170.64 (define @t177 () (@var "T" tptp.term)) % 170.30/170.64 (define @t178 () (= @t177 @t176)) % 170.30/170.64 (define @t179 () (exists @t174 @t178)) % 170.30/170.64 (define @t180 () (@list @t177)) % 170.30/170.64 (define @t181 () (forall @t180 @t179)) % 170.30/170.64 (define @t182 () (_ (_ @t3 @t72) tptp.id)) % 170.30/170.64 (define @t183 () (=> @t29 @t182)) % 170.30/170.64 (define @t184 () (forall @t32 (=> @t9 @t183))) % 170.30/170.64 (define @t185 () (_ (_ (_ (_ tptp.hoasap tptp.id) @t8) tptp.id) @t24)) % 170.30/170.64 (define @t186 () (_ (_ @t3 @t185) tptp.id)) % 170.30/170.64 (define @t187 () (=> @t29 @t186)) % 170.30/170.64 (define @t188 () (forall @t32 (=> @t9 @t187))) % 170.30/170.64 (define @t189 () (=> @t188 @t184)) % 170.30/170.64 (define @t190 () (forall @t44 (=> @t41 @t38))) % 170.30/170.64 (define @t191 () (=> @t190 @t189)) % 170.30/170.64 (define @t192 () (forall @t44 (=> @t38 @t41))) % 170.30/170.64 (define @t193 () (=> @t192 @t191)) % 170.30/170.64 (define @t194 () (forall @t79 @t193)) % 170.30/170.64 (define @t195 () (= tptp.hoasinduction_lem2 @t194)) % 170.30/170.64 (define @t196 () (not @t195)) % 170.30/170.64 (define @t197 () (@const 0 (@ho-elim-sort (-> tptp.d_term tptp.term)))) % 170.30/170.64 (define @t198 () (@const 1 (-> (@ho-elim-sort (-> tptp.d_term tptp.term)) tptp.d_term tptp.term))) % 170.30/170.64 (define @t199 () (_ @t198 @t197 @t173)) % 170.30/170.64 (define @t200 () (forall @t180 (not (forall @t174 (not (= @t177 @t199)))))) % 170.30/170.64 (define @t201 () (tptp.d2term @t173)) % 170.30/170.64 (define @t202 () (not @t178)) % 170.30/170.64 (define @t203 () (forall @t174 @t202)) % 170.30/170.64 (define @t204 () (not @t203)) % 170.30/170.64 (define @t205 () (_ (@const 3 (-> (@ho-elim-sort (-> tptp.d_subst tptp.subst)) tptp.d_subst tptp.subst)) (@const 2 (@ho-elim-sort (-> tptp.d_subst tptp.subst))) tptp.d_id)) % 170.30/170.64 (define @t206 () (@var "BOUND_VARIABLE_9053" tptp.term)) % 170.30/170.64 (define @t207 () (@var "BOUND_VARIABLE_9051" tptp.term)) % 170.30/170.64 (define @t208 () (@const 4 (@ho-elim-sort (-> tptp.term tptp.term tptp.term)))) % 170.30/170.64 (define @t209 () (@const 5 (-> (@ho-elim-sort (-> tptp.term tptp.term tptp.term)) tptp.term (@ho-elim-sort (-> tptp.term tptp.term))))) % 170.30/170.64 (define @t210 () (@const 6 (-> (@ho-elim-sort (-> tptp.term tptp.term)) tptp.term tptp.term))) % 170.30/170.64 (define @t211 () (@var "BOUND_VARIABLE_10145" (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool)))) % 170.30/170.64 (define @t212 () (@const 7 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst Bool)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.subst Bool))))) % 170.30/170.64 (define @t213 () (_ @t212 @t211 @t205)) % 170.30/170.64 (define @t214 () (@const 8 (-> (@ho-elim-sort (-> tptp.term tptp.subst Bool)) tptp.term (@ho-elim-sort (-> tptp.subst Bool))))) % 170.30/170.64 (define @t215 () (@const 9 (-> (@ho-elim-sort (-> tptp.subst Bool)) tptp.subst Bool))) % 170.30/170.64 (define @t216 () (_ (@const 11 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.subst tptp.term tptp.term)))) (@const 10 (@ho-elim-sort (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term))) @t205)) % 170.30/170.64 (define @t217 () (@const 12 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term tptp.term))))) % 170.30/170.64 (define @t218 () (@const 13 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.term)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.term))))) % 170.30/170.64 (define @t219 () (_ @t210 (_ @t218 (_ @t217 @t216 @t8) @t205) @t24)) % 170.30/170.64 (define @t220 () (not (_ @t215 (_ @t214 @t213 @t24) @t205))) % 170.30/170.64 (define @t221 () (not (_ @t215 (_ @t214 @t213 @t8) @t205))) % 170.30/170.64 (define @t222 () (@const 14 (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)))) % 170.30/170.64 (define @t223 () (@const 15 (-> (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)) tptp.subst (@ho-elim-sort (-> tptp.subst tptp.subst))))) % 170.30/170.64 (define @t224 () (@const 16 (-> (@ho-elim-sort (-> tptp.subst tptp.subst)) tptp.subst tptp.subst))) % 170.30/170.64 (define @t225 () (_ @t224 (_ @t223 @t222 @t35) @t13)) % 170.30/170.64 (define @t226 () (_ @t215 (_ @t214 (_ @t212 @t211 @t16) @t8) @t225)) % 170.30/170.64 (define @t227 () (@const 17 (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)))) % 170.30/170.64 (define @t228 () (@const 18 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term))))) % 170.30/170.64 (define @t229 () (_ @t228 @t227 @t8)) % 170.30/170.64 (define @t230 () (@const 19 (-> (@ho-elim-sort (-> tptp.subst tptp.term)) tptp.subst tptp.term))) % 170.30/170.64 (define @t231 () (_ @t230 @t229 @t35)) % 170.30/170.64 (define @t232 () (_ @t224 (_ @t223 @t222 @t16) @t35)) % 170.30/170.64 (define @t233 () (_ @t215 (_ @t214 (_ @t212 @t211 @t232) @t231) @t13)) % 170.30/170.64 (define @t234 () (not (forall @t44 (or (not @t233) @t226)))) % 170.30/170.64 (define @t235 () (not (forall @t44 (or (not @t226) @t233)))) % 170.30/170.64 (define @t236 () (forall (@list @t211 @t207 @t206) (or @t235 @t234 (not (forall @t32 (or @t221 @t220 (_ @t215 (_ @t214 @t213 @t219) @t205)))) (not (_ @t215 (_ @t214 @t213 @t207) @t205)) (not (_ @t215 (_ @t214 @t213 @t206) @t205)) (_ @t215 (_ @t214 @t213 (_ @t210 (_ @t209 @t208 @t207) @t206)) @t205)))) % 170.30/170.64 (define @t237 () (@quantifiers_skolemize @t236 1)) % 170.30/170.64 (define @t238 () (not (= @t237 @t199))) % 170.30/170.64 (define @t239 () (forall @t174 @t238)) % 170.30/170.64 (define @t240 () (not @t239)) % 170.30/170.64 (define @t241 () (forall @t174 (not (= @t199 @t237)))) % 170.30/170.64 (define @t242 () (not @t241)) % 170.30/170.64 (define @t243 () (@list false)) % 170.30/170.64 (define @t244 () (@list @t200)) % 170.30/170.64 (define @t245 () (@quantifiers_skolemize @t241 0)) % 170.30/170.64 (define @t246 () (_ @t198 @t197 @t245)) % 170.30/170.64 (define @t247 () (= @t237 @t246)) % 170.30/170.64 (define @t248 () (= @t246 @t237)) % 170.30/170.64 (define @t249 () (not (not @t248))) % 170.30/170.64 (define @t250 () (@list true)) % 170.30/170.64 (define @t251 () (_ @t210 (_ @t209 @t208 (_ @t230 @t229 @t205)) @t24)) % 170.30/170.64 (define @t252 () (forall (@list @t211 @t140 @t139) (or @t235 @t234 (not (forall @t32 (or @t221 @t220 (_ @t215 (_ @t214 @t213 @t251) @t205)))) (not (_ @t215 (_ @t214 @t213 @t140) @t205)) (not (_ @t215 (_ @t214 @t213 @t139) @t205)) (_ @t215 (_ @t214 @t213 (_ @t210 (_ @t209 @t208 @t140) @t139)) @t205)))) % 170.30/170.64 (define @t253 () (@quantifiers_skolemize @t252 0)) % 170.30/170.64 (define @t254 () (_ @t212 @t253 @t205)) % 170.30/170.64 (define @t255 () (forall @t32 (or (not (_ @t215 (_ @t214 @t254 @t8) @t205)) (not (_ @t215 (_ @t214 @t254 @t24) @t205)) (_ @t215 (_ @t214 @t254 @t251) @t205)))) % 170.30/170.64 (define @t256 () (@quantifiers_skolemize @t252 2)) % 170.30/170.64 (define @t257 () (@quantifiers_skolemize @t252 1)) % 170.30/170.64 (define @t258 () (_ @t209 @t208 @t257)) % 170.30/170.64 (define @t259 () (_ @t210 @t258 @t256)) % 170.30/170.64 (define @t260 () (_ @t214 @t254 @t259)) % 170.30/170.64 (define @t261 () (_ @t215 @t260 @t205)) % 170.30/170.64 (define @t262 () (_ @t215 (_ @t214 @t254 @t256) @t205)) % 170.30/170.64 (define @t263 () (not @t262)) % 170.30/170.64 (define @t264 () (_ @t215 (_ @t214 @t254 @t257) @t205)) % 170.30/170.64 (define @t265 () (not @t264)) % 170.30/170.64 (define @t266 () (not @t255)) % 170.30/170.64 (define @t267 () (_ @t215 (_ @t214 (_ @t212 @t253 @t16) @t8) @t225)) % 170.30/170.64 (define @t268 () (_ @t215 (_ @t214 (_ @t212 @t253 @t232) @t231) @t13)) % 170.30/170.64 (define @t269 () (or (not (forall @t44 (or (not @t267) @t268))) (not (forall @t44 (or (not @t268) @t267))) @t266 @t265 @t263 @t261)) % 170.30/170.64 (define @t270 () (_ @t215 (_ @t214 @t254 (_ @t210 (_ @t209 @t208 (_ @t230 (_ @t228 @t227 @t257) @t205)) @t256)) @t205)) % 170.30/170.64 (define @t271 () (or @t265 @t263 @t270)) % 170.30/170.64 (define @t272 () (_ @t198 @t197 tptp.d_one)) % 170.30/170.64 (define @t273 () (_ @t228 @t227 @t272)) % 170.30/170.64 (define @t274 () (_ @t230 @t273 @t205)) % 170.30/170.64 (define @t275 () (= @t272 @t274)) % 170.30/170.64 (define @t276 () (not (= @t257 @t199))) % 170.30/170.64 (define @t277 () (forall @t174 @t276)) % 170.30/170.64 (define @t278 () (not @t277)) % 170.30/170.64 (define @t279 () (forall @t174 (not (= @t199 @t257)))) % 170.30/170.64 (define @t280 () (not @t279)) % 170.30/170.64 (define @t281 () (@quantifiers_skolemize @t279 0)) % 170.30/170.64 (define @t282 () (_ @t198 @t197 @t281)) % 170.30/170.64 (define @t283 () (= @t257 @t282)) % 170.30/170.64 (define @t284 () (= @t282 @t257)) % 170.30/170.64 (define @t285 () (not (not @t284))) % 170.30/170.64 (define @t286 () (not @t270)) % 170.30/170.64 (define @t287 () (= tptp.d_one @t281)) % 170.30/170.64 (define @t288 () (not @t287)) % 170.30/170.64 (define @t289 () (not @t283)) % 170.30/170.64 (define @t290 () (not @t275)) % 170.30/170.64 (define @t291 () (not @t261)) % 170.30/170.64 (define @t292 () (= false true)) % 170.30/170.64 (define @t293 () (_ @t209 @t208 @t274)) % 170.30/170.64 (define @t294 () (_ @t209 @t208 @t272)) % 170.30/170.64 (define @t295 () (and @t270 @t283 @t287 @t275 @t291)) % 170.30/170.64 (define @t296 () (not @t269)) % 170.30/170.64 (define @t297 () (not @t252)) % 170.30/170.64 (define @t298 () (not (= @t252 @t236))) % 170.30/170.64 (define @t299 () (tptp.d2subst tptp.d_id)) % 170.30/170.64 (define @t300 () (tptp.ap @t207 @t206)) % 170.30/170.64 (define @t301 () (not (_ @t2 @t299 @t24 @t299))) % 170.30/170.64 (define @t302 () (not (_ @t2 @t299 @t8 @t299))) % 170.30/170.64 (define @t303 () (not (forall @t32 (or @t302 @t301 (_ @t2 @t299 (tptp.hoasap @t299 @t8 @t299 @t24) @t299))))) % 170.30/170.64 (define @t304 () (tptp.comp @t35 @t13)) % 170.30/170.64 (define @t305 () (_ @t2 @t16 @t8 @t304)) % 170.30/170.64 (define @t306 () (tptp.sub @t8 @t35)) % 170.30/170.64 (define @t307 () (tptp.comp @t16 @t35)) % 170.30/170.64 (define @t308 () (_ @t2 @t307 @t306 @t13)) % 170.30/170.64 (define @t309 () (forall @t44 (or (not @t308) @t305))) % 170.30/170.64 (define @t310 () (not @t309)) % 170.30/170.64 (define @t311 () (forall @t44 (or (not @t305) @t308))) % 170.30/170.64 (define @t312 () (not @t311)) % 170.30/170.64 (define @t313 () (@list @t2 @t207 @t206)) % 170.30/170.64 (define @t314 () (tptp.ap @t140 @t139)) % 170.30/170.64 (define @t315 () (not (forall @t32 (or @t302 @t301 (_ @t2 @t299 (tptp.ap (tptp.sub @t8 @t299) @t24) @t299))))) % 170.30/170.64 (define @t316 () (forall @t148 (or @t312 @t310 @t315 (not (_ @t2 @t299 @t140 @t299)) (not (_ @t2 @t299 @t139 @t299)) (_ @t2 @t299 @t314 @t299)))) % 170.30/170.64 (define @t317 () (_ @t2 @t96 @t300 @t96)) % 170.30/170.64 (define @t318 () (_ @t2 @t96 @t206 @t96)) % 170.30/170.64 (define @t319 () (not @t318)) % 170.30/170.64 (define @t320 () (_ @t2 @t96 @t207 @t96)) % 170.30/170.64 (define @t321 () (not @t320)) % 170.30/170.64 (define @t322 () (or @t312 @t310 @t303 @t321 @t319 @t317)) % 170.30/170.64 (define @t323 () (tptp.hoasap @t96 @t8 @t96 @t24)) % 170.30/170.64 (define @t324 () (_ @t2 @t96 @t323 @t96)) % 170.30/170.64 (define @t325 () (_ @t2 @t96 @t24 @t96)) % 170.30/170.64 (define @t326 () (not @t325)) % 170.30/170.64 (define @t327 () (_ @t2 @t96 @t8 @t96)) % 170.30/170.64 (define @t328 () (not @t327)) % 170.30/170.64 (define @t329 () (or @t328 @t326 @t324)) % 170.30/170.64 (define @t330 () (forall @t32 @t329)) % 170.30/170.64 (define @t331 () (not @t330)) % 170.30/170.64 (define @t332 () (or @t312 @t310 @t331 @t321 @t319 @t317)) % 170.30/170.64 (define @t333 () (forall @t313 @t332)) % 170.30/170.64 (define @t334 () (= @t316 @t333)) % 170.30/170.64 (define @t335 () (_ @t2 tptp.id @t300 tptp.id)) % 170.30/170.64 (define @t336 () (_ @t2 tptp.id @t206 tptp.id)) % 170.30/170.64 (define @t337 () (not @t336)) % 170.30/170.64 (define @t338 () (_ @t2 tptp.id @t207 tptp.id)) % 170.30/170.64 (define @t339 () (not @t338)) % 170.30/170.64 (define @t340 () (tptp.hoasap tptp.id @t8 tptp.id @t24)) % 170.30/170.64 (define @t341 () (_ @t2 tptp.id @t340 tptp.id)) % 170.30/170.64 (define @t342 () (_ @t2 tptp.id @t24 tptp.id)) % 170.30/170.64 (define @t343 () (not @t342)) % 170.30/170.64 (define @t344 () (_ @t2 tptp.id @t8 tptp.id)) % 170.30/170.64 (define @t345 () (not @t344)) % 170.30/170.64 (define @t346 () (or @t345 @t343 @t341)) % 170.30/170.64 (define @t347 () (forall @t32 @t346)) % 170.30/170.64 (define @t348 () (not @t347)) % 170.30/170.64 (define @t349 () (or @t312 @t310 @t348 @t339 @t337 @t335)) % 170.30/170.64 (define @t350 () (forall @t313 @t349)) % 170.30/170.64 (define @t351 () (_ @t2 @t96 @t314 @t96)) % 170.30/170.64 (define @t352 () (_ @t2 @t96 @t139 @t96)) % 170.30/170.64 (define @t353 () (not @t352)) % 170.30/170.64 (define @t354 () (_ @t2 @t96 @t140 @t96)) % 170.30/170.64 (define @t355 () (not @t354)) % 170.30/170.64 (define @t356 () (or @t312 @t310 @t315 @t355 @t353 @t351)) % 170.30/170.64 (define @t357 () (tptp.sub @t8 @t96)) % 170.30/170.64 (define @t358 () (tptp.ap @t357 @t24)) % 170.30/170.64 (define @t359 () (_ @t2 @t96 @t358 @t96)) % 170.30/170.64 (define @t360 () (or @t328 @t326 @t359)) % 170.30/170.64 (define @t361 () (forall @t32 @t360)) % 170.30/170.64 (define @t362 () (not @t361)) % 170.30/170.64 (define @t363 () (or @t312 @t310 @t362 @t355 @t353 @t351)) % 170.30/170.64 (define @t364 () (forall @t148 @t363)) % 170.30/170.64 (define @t365 () (_ @t2 tptp.id @t314 tptp.id)) % 170.30/170.64 (define @t366 () (_ @t2 tptp.id @t139 tptp.id)) % 170.30/170.64 (define @t367 () (not @t366)) % 170.30/170.64 (define @t368 () (_ @t2 tptp.id @t140 tptp.id)) % 170.30/170.64 (define @t369 () (not @t368)) % 170.30/170.64 (define @t370 () (tptp.sub @t8 tptp.id)) % 170.30/170.64 (define @t371 () (tptp.ap @t370 @t24)) % 170.30/170.64 (define @t372 () (_ @t2 tptp.id @t371 tptp.id)) % 170.30/170.64 (define @t373 () (or @t345 @t343 @t372)) % 170.30/170.64 (define @t374 () (forall @t32 @t373)) % 170.30/170.64 (define @t375 () (not @t374)) % 170.30/170.64 (define @t376 () (or @t312 @t310 @t375 @t369 @t367 @t365)) % 170.30/170.64 (define @t377 () (forall @t148 @t376)) % 170.30/170.64 (define @t378 () (or @t312 @t310 @t375 @t146 @t144 @t142)) % 170.30/170.64 (define @t379 () (= tptp.hoasinduction_lem2 @t350)) % 170.30/170.64 (define @t380 () (or @t339 @t337 @t335)) % 170.30/170.64 (define @t381 () (or @t312 @t310 @t348 @t380)) % 170.30/170.64 (define @t382 () (forall @t313 @t381)) % 170.30/170.64 (define @t383 () (@list @t207 @t206)) % 170.30/170.64 (define @t384 () (forall @t383 @t381)) % 170.30/170.64 (define @t385 () (forall @t383 @t380)) % 170.30/170.64 (define @t386 () (or @t312 @t310 @t348 @t385)) % 170.30/170.64 (define @t387 () (tptp.ap @t8 @t24)) % 170.30/170.64 (define @t388 () (_ @t2 tptp.id @t387 tptp.id)) % 170.30/170.64 (define @t389 () (forall @t32 (or @t345 @t343 @t388))) % 170.30/170.64 (define @t390 () (or @t312 @t310 @t348 @t389)) % 170.30/170.64 (define @t391 () (or @t310 @t348 @t389)) % 170.30/170.64 (define @t392 () (=> @t347 @t389)) % 170.30/170.64 (define @t393 () (=> @t309 @t392)) % 170.30/170.64 (define @t394 () (or @t10 @t30 @t182)) % 170.30/170.64 (define @t395 () (or @t10 @t30 @t186)) % 170.30/170.64 (define @t396 () (not @t236)) % 170.30/170.64 (define @t397 () (@quantifiers_skolemize @t236 2)) % 170.30/170.64 (define @t398 () (_ @t209 @t208 @t237)) % 170.30/170.64 (define @t399 () (_ @t210 @t398 @t397)) % 170.30/170.64 (define @t400 () (@quantifiers_skolemize @t236 0)) % 170.30/170.64 (define @t401 () (_ @t212 @t400 @t205)) % 170.30/170.64 (define @t402 () (_ @t214 @t401 @t399)) % 170.30/170.64 (define @t403 () (_ @t215 @t402 @t205)) % 170.30/170.64 (define @t404 () (_ @t215 (_ @t214 @t401 @t397) @t205)) % 170.30/170.64 (define @t405 () (not @t404)) % 170.30/170.64 (define @t406 () (_ @t215 (_ @t214 @t401 @t237) @t205)) % 170.30/170.64 (define @t407 () (not @t406)) % 170.30/170.64 (define @t408 () (forall @t32 (or (not (_ @t215 (_ @t214 @t401 @t8) @t205)) (not (_ @t215 (_ @t214 @t401 @t24) @t205)) (_ @t215 (_ @t214 @t401 @t219) @t205)))) % 170.30/170.64 (define @t409 () (not @t408)) % 170.30/170.64 (define @t410 () (_ @t215 (_ @t214 (_ @t212 @t400 @t16) @t8) @t225)) % 170.30/170.64 (define @t411 () (_ @t215 (_ @t214 (_ @t212 @t400 @t232) @t231) @t13)) % 170.30/170.64 (define @t412 () (or (not (forall @t44 (or (not @t410) @t411))) (not (forall @t44 (or (not @t411) @t410))) @t409 @t407 @t405 @t403)) % 170.30/170.64 (define @t413 () (not @t412)) % 170.30/170.64 (define @t414 () (@list @t412)) % 170.30/170.64 (define @t415 () (_ @t215 (_ @t214 @t401 (_ @t210 (_ @t218 (_ @t217 @t216 @t237) @t205) @t397)) @t205)) % 170.30/170.64 (define @t416 () (or @t407 @t405 @t415)) % 170.30/170.64 (define @t417 () (not @t403)) % 170.30/170.64 (define @t418 () (@var "y" (@ho-elim-sort (-> tptp.term tptp.term)))) % 170.30/170.64 (define @t419 () (@var "x" (@ho-elim-sort (-> tptp.term tptp.term)))) % 170.30/170.64 (define @t420 () (@var "z" tptp.term)) % 170.30/170.64 (define @t421 () (@list @t420)) % 170.30/170.64 (define @t422 () (_ @t217 @t216 @t272)) % 170.30/170.64 (define @t423 () (_ @t218 @t422 @t205)) % 170.30/170.64 (define @t424 () (forall @t421 (= (_ @t210 @t294 @t420) (_ @t210 @t423 @t420)))) % 170.30/170.64 (define @t425 () (@quantifiers_skolemize @t424 0)) % 170.30/170.64 (define @t426 () (not (= @t425 @t199))) % 170.30/170.64 (define @t427 () (forall @t174 @t426)) % 170.30/170.64 (define @t428 () (not @t427)) % 170.30/170.64 (define @t429 () (forall @t174 (not (= @t199 @t425)))) % 170.30/170.64 (define @t430 () (not @t429)) % 170.30/170.64 (define @t431 () (@quantifiers_skolemize @t429 0)) % 170.30/170.64 (define @t432 () (_ @t198 @t197 @t431)) % 170.30/170.64 (define @t433 () (= @t425 @t432)) % 170.30/170.64 (define @t434 () (= @t432 @t425)) % 170.30/170.64 (define @t435 () (not (not @t434))) % 170.30/170.64 (define @t436 () (_ @t210 @t423 @t272)) % 170.30/170.64 (define @t437 () (_ @t210 @t294 @t425)) % 170.30/170.64 (define @t438 () (= @t437 (_ @t210 @t423 @t425))) % 170.30/170.64 (define @t439 () (not @t438)) % 170.30/170.64 (define @t440 () (not @t424)) % 170.30/170.64 (define @t441 () (= @t294 @t423)) % 170.30/170.64 (define @t442 () (or @t440 @t441)) % 170.30/170.64 (define @t443 () (not @t415)) % 170.30/170.64 (define @t444 () (= @t272 @t237)) % 170.30/170.64 (define @t445 () (not @t444)) % 170.30/170.64 (define @t446 () (not @t441)) % 170.30/170.64 (define @t447 () (@list @t245)) % 170.30/170.64 (define @t448 () (and @t415 @t444 @t441 @t275 @t417)) % 170.30/170.64 (define @t449 () (= tptp.d_one @t245)) % 170.30/170.64 (define @t450 () (and @t247 @t449)) % 170.30/170.64 (assume @p1 (and @t181 @t175 (forall (@list @t172 @t171) (=> (= (_ tptp.d2term @t172) (_ tptp.d2term @t171)) (= @t172 @t171))) (forall (@list @t170) (exists @t169 (= @t170 (_ tptp.d2subst @t168)))) (forall @t169 (= @t168 tptp.d_id)) (forall (@list @t167 @t166) (=> (= (_ tptp.d2subst @t167) (_ tptp.d2subst @t166)) (= @t167 @t166))) (= tptp.one @t97) (= @t165 @t97) (= (_ tptp.lam @t97) @t97) (= @t164 @t97) (= tptp.id @t96) (= tptp.sh @t96) (= (_ (_ tptp.push @t97) @t96) @t96) (= (_ (_ tptp.comp @t96) @t96) @t96) (= @t163 @t97) (= tptp.hoaslam (lambda (@list (@var "Bound_variable_4913" tptp.subst) (@var "Bound_variable_4915" (-> tptp.subst tptp.term tptp.term))) @t97)) (= tptp.hoasinduction_p_and_p_prime (lambda (@list @t2 @t53) @t61)) (= tptp.pushprop_p_and_p_prime (lambda (@list @t8 @t16 @t66 @t53) @t84)) (not (_ tptp.var @t97)) (= tptp.pushprop_lem1v2 @t138) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t32 (or (not (= (_ @t14 tptp.sh) (_ @t107 tptp.sh))) @t118))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t111) (= tptp.hoasinduction_lem3v2_f @t112) tptp.axvarshift (= tptp.hoasapinj2 @t132) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t128) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t93 (=> @t89 (=> @t103 (=> @t137 @t111))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t112) (= tptp.hoasinduction_lthm (=> @t77 (=> @t149 (=> @t114 @t51)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t80 (=> @t77 (=> @t64 (=> @t63 @t99))))) (= tptp.hoaslaminj @t123) (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t151) (or (not (forall (@list @t4 @t158) (or @t12 @t7 (not (forall (@list @t161 @t162 @t160) (= (_ (_ tptp.sub (_ (_ @t4 @t161) @t162)) @t160) (_ (_ tptp.sub (_ @t159 (_ (_ tptp.push @t162) @t161))) @t160)))) (not (forall (@list @t154 @t156 @t153) (= (_ (_ @t4 @t155) @t157) (_ @t159 (_ (_ tptp.push @t157) @t155)))))))) (not (forall @t57 (or @t30 (_ (_ @t3 (_ @t152 @t55)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t152 @t106))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t117) (= tptp.hoasinduction_lem3 @t114) @t150 (= tptp.termmset_lthm (=> @t64 @t64)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t93 @t138)) tptp.hoasapnotvar (= tptp.hoasinduction_lem0 @t80) (= tptp.hoasinduction @t51) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t108) tptp.ulamvarind (= tptp.induction @t137) (= tptp.hoasinduction_lem3a_lthm (=> @t64 (=> @t117 @t101))) tptp.termmset_gthm (= tptp.hoasinduction_lem3aa @t117) 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 @t53 @t135 @t134) (or @t50 @t46 @t34 @t62 (not (_ @t53 @t135)) (not (_ @t53 @t134)) (_ @t53 (_ (_ tptp.ap @t135) @t134))))) tptp.pushprop_lthm (= tptp.apinj2 @t133) (= tptp.apinj1 @t130) (= tptp.hoasapinj2_lthm (=> @t133 @t132)) (= tptp.hoasinduction_lem3v2a @t63) (= tptp.hoasapinj1_lthm (=> @t64 (=> @t130 @t128))) (= tptp.hoaslaminj_lthm (=> @t93 (=> @t89 (=> @t119 @t123)))) (= tptp.axvarcons @t93) (= tptp.axscons (forall @t102 (= @t16 (_ (_ tptp.push (_ @t92 @t16)) (_ @t87 @t16))))) tptp.hoasinduction_lem2v2_gthm (= tptp.axidr @t103) (= tptp.pushprop_lem1 @t91) (= tptp.laminj @t119) (= tptp.hoasinduction_lem3_lthm (=> @t64 (=> @t117 @t114))) (= tptp.pushprop_lem0 @t86) tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t112 (=> @t64 @t63))) tptp.hoasinduction_lem2_lthm tptp.hoasapinj2_gthm tptp.hoasinduction_lem1_lthm (not tptp.lamnotap) tptp.hoasapinj1_gthm tptp.hoaslamnotvar (= tptp.axidl @t104) tptp.hoaslaminj_gthm (= tptp.induction2_lthm (=> @t64 (=> @t111 @t77))) (= tptp.hoasinduction_lem0_lthm @t80) (= tptp.substmonoid_lthm (=> @t104 (=> @t103 @t105))) tptp.pushprop tptp.hoasinduction_lem3_gthm tptp.hoasinduction_lem2_gthm (= tptp.hoasinduction_lem3b @t108) (= tptp.substmonoid @t105) tptp.lamnotvar (= tptp.hoasinduction_lem3a @t101) tptp.hoasinduction_lem1_gthm (= tptp.hoasinduction_no_psi_cond @t99) tptp.induction2_gthm tptp.pushprop_lem2v2_lthm (not (_ (_ (_ tptp.hoasvar @t96) @t97) @t96)) (= tptp.hoaslamnotap (forall (@list @t4 @t95 @t94) (or @t21 (not (= @t6 (_ (_ tptp.ap (_ (_ tptp.sub @t95) tptp.id)) @t94)))))) tptp.substmonoid_gthm tptp.ulamvarsh (= tptp.induction2 @t77) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t93 (=> @t89 @t91))) (= tptp.hoasinduction_lem3v2 @t82) (= tptp.axshiftcons @t89) (= tptp.termmset @t64) (= tptp.pushprop_lem0_lthm @t86) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t64 @t82)) (= tptp.axvarid @t64) (= tptp.hoasinduction_lthm_3 (=> @t80 (=> @t77 (=> @t64 (=> @t63 @t51))))))) % 170.30/170.64 (assume @p2 @t196) % 170.30/170.64 (assume @p3 true) % 170.30/170.64 ; WARNING: add trust step for TRUST % 170.30/170.64 ; trust TRUST PREPROCESS_HO_ELIM % 170.30/170.64 (step @p4 :rule trust :premises () :args ((= (forall @t180 (not (forall @t174 (not (= @t177 @t201))))) @t200))) % 170.30/170.64 (step @p5 :rule refl :args (@t201)) % 170.30/170.64 (step @p6 :rule refl :args (@t176)) % 170.30/170.64 (step @p7 :rule cong :premises (@p6 @p5) :args ((= @t176 @t201))) % 170.30/170.64 (step @p8 :rule symm :premises (@p7)) % 170.30/170.64 (step @p9 :rule eq_resolve :premises (@p6 @p8)) % 170.30/170.64 (step @p10 :rule refl :args (@t177)) % 170.30/170.64 (step @p11 :rule cong :premises (@p10 @p9) :args (@t178)) % 170.30/170.64 (step @p12 :rule cong :premises (@p11) :args (@t202)) % 170.30/170.64 (step @p13 :rule cong :premises (@p12) :args (@t203)) % 170.30/170.64 (step @p14 :rule cong :premises (@p13) :args (@t204)) % 170.30/170.64 (step @p15 :rule exists-elim :args ((= @t179 @t204))) % 170.30/170.64 (step @p16 :rule trans :premises (@p15 @p14)) % 170.30/170.64 (step @p17 :rule cong :premises (@p16) :args (@t181)) % 170.30/170.64 (step @p18 :rule trans :premises (@p17 @p4)) % 170.30/170.64 (step @p19 :rule and_elim :premises (@p1) :args (0)) % 170.30/170.64 (step @p20 :rule eq_resolve :premises (@p19 @p18)) % 170.30/170.64 (step @p21 :rule eq-symm :args (@t237 @t199)) % 170.30/170.64 (step @p22 :rule cong :premises (@p21) :args (@t238)) % 170.30/170.64 (step @p23 :rule cong :premises (@p22) :args (@t239)) % 170.30/170.64 (step @p24 :rule cong :premises (@p23) :args (@t240)) % 170.30/170.64 (step @p25 :rule refl :args (@t200)) % 170.30/170.64 (step @p26 :rule cong :premises (@p25 @p24) :args ((=> @t200 @t240))) % 170.30/170.64 (assume-push @p707 @t200) % 170.30/170.64 (step @p28 :rule instantiate :premises (@p20) :args ((@list @t237))) % 170.30/170.64 (step-pop @p708 :rule scope :premises (@p28)) % 170.30/170.64 (step @p29 :rule process_scope :premises (@p708) :args (@t240)) % 170.30/170.64 (step @p31 :rule eq_resolve :premises (@p29 @p26)) % 170.30/170.64 (step @p32 :rule implies_elim :premises (@p31)) % 170.30/170.64 (step @p33 :rule chain_m_resolution :premises (@p32 @p20) :args (@t242 @t243 @t244)) % 170.30/170.64 (step @p34 :rule refl :args (@t247)) % 170.30/170.64 (step @p35 :rule bool-double-not-elim :args (@t241)) % 170.30/170.64 (step @p36 :rule nary_cong :premises (@p35 @p34) :args ((or (not @t242) @t247))) % 170.30/170.64 (step @p37 :rule eq-symm :args (@t246 @t237)) % 170.30/170.64 (step @p38 :rule bool-double-not-elim :args (@t248)) % 170.30/170.64 (step @p39 :rule trans :premises (@p38 @p37)) % 170.30/170.64 (step @p40 :rule refl :args (@t242)) % 170.30/170.64 (step @p41 :rule cong :premises (@p40 @p39) :args ((=> @t242 @t249))) % 170.30/170.64 (assume-push @p709 @t242) % 170.30/170.64 (step @p43 :rule skolemize :premises (@p33)) % 170.30/170.64 (step-pop @p710 :rule scope :premises (@p43)) % 170.30/170.64 (step @p44 :rule process_scope :premises (@p710) :args (@t249)) % 170.30/170.64 (step @p46 :rule eq_resolve :premises (@p44 @p41)) % 170.30/170.64 (step @p47 :rule implies_elim :premises (@p46)) % 170.30/170.64 (step @p48 :rule eq_resolve :premises (@p47 @p36)) % 170.30/170.64 (step @p49 :rule chain_m_resolution :premises (@p48 @p33) :args (@t247 @t250 (@list @t241))) % 170.30/170.64 (step @p50 :rule bool-double-not-elim :args (@t255)) % 170.30/170.64 (step @p51 :rule refl :args (@t269)) % 170.30/170.64 (step @p52 :rule nary_cong :premises (@p51 @p50) :args ((or @t269 (not @t266)))) % 170.30/170.64 (step @p53 :rule cnf_or_neg :args (@t269 2)) % 170.30/170.64 (step @p54 :rule eq_resolve :premises (@p53 @p52)) % 170.30/170.64 (step @p55 :rule reordering :premises (@p54) :args ((or @t255 @t269))) % 170.30/170.64 (step @p56 :rule bool-double-not-elim :args (@t264)) % 170.30/170.64 (step @p57 :rule nary_cong :premises (@p51 @p56) :args ((or @t269 (not @t265)))) % 170.30/170.64 (step @p58 :rule cnf_or_neg :args (@t269 3)) % 170.30/170.64 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 170.30/170.64 (step @p60 :rule reordering :premises (@p59) :args ((or @t264 @t269))) % 170.30/170.64 (step @p61 :rule bool-double-not-elim :args (@t262)) % 170.30/170.64 (step @p62 :rule nary_cong :premises (@p51 @p61) :args ((or @t269 (not @t263)))) % 170.30/170.64 (step @p63 :rule cnf_or_neg :args (@t269 4)) % 170.30/170.64 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 170.30/170.64 (step @p65 :rule reordering :premises (@p64) :args ((or @t262 @t269))) % 170.30/170.64 (step @p66 :rule cnf_or_neg :args (@t269 5)) % 170.30/170.64 (assume-push @p711 @t255) % 170.30/170.64 (step @p68 :rule instantiate :premises (@p711) :args ((@list @t257 @t256))) % 170.30/170.64 (step-pop @p712 :rule scope :premises (@p68)) % 170.30/170.64 (step @p69 :rule process_scope :premises (@p712) :args (@t271)) % 170.30/170.64 (step @p71 :rule implies_elim :premises (@p69)) % 170.30/170.64 (step @p72 :rule cnf_or_pos :args (@t271)) % 170.30/170.64 (step @p73 :rule reordering :premises (@p72) :args ((or @t265 @t263 @t270 (not @t271)))) % 170.30/170.64 ; trust TRUST PREPROCESS_HO_ELIM % 170.30/170.64 (step @p74 :rule trust :premises () :args ((= (= @t97 @t164) @t275))) % 170.30/170.64 (step @p75 :rule eq-symm :args (@t164 @t97)) % 170.30/170.64 (step @p76 :rule trans :premises (@p75 @p74)) % 170.30/170.64 (step @p77 :rule and_elim :premises (@p1) :args (9)) % 170.30/170.64 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 170.30/170.64 (step @p79 :rule eq-symm :args (@t257 @t199)) % 170.30/170.64 (step @p80 :rule cong :premises (@p79) :args (@t276)) % 170.30/170.64 (step @p81 :rule cong :premises (@p80) :args (@t277)) % 170.30/170.64 (step @p82 :rule cong :premises (@p81) :args (@t278)) % 170.30/170.64 (step @p83 :rule cong :premises (@p25 @p82) :args ((=> @t200 @t278))) % 170.30/170.64 (assume-push @p713 @t200) % 170.30/170.64 (step @p85 :rule instantiate :premises (@p20) :args ((@list @t257))) % 170.30/170.64 (step-pop @p714 :rule scope :premises (@p85)) % 170.30/170.64 (step @p86 :rule process_scope :premises (@p714) :args (@t278)) % 170.30/170.64 (step @p88 :rule eq_resolve :premises (@p86 @p83)) % 170.30/170.64 (step @p89 :rule implies_elim :premises (@p88)) % 170.30/170.64 (step @p90 :rule chain_m_resolution :premises (@p89 @p20) :args (@t280 @t243 @t244)) % 170.30/170.64 (step @p91 :rule refl :args (@t283)) % 170.30/170.64 (step @p92 :rule bool-double-not-elim :args (@t279)) % 170.30/170.64 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or (not @t280) @t283))) % 170.30/170.64 (step @p94 :rule eq-symm :args (@t282 @t257)) % 170.30/170.64 (step @p95 :rule bool-double-not-elim :args (@t284)) % 170.30/170.64 (step @p96 :rule trans :premises (@p95 @p94)) % 170.30/170.64 (step @p97 :rule refl :args (@t280)) % 170.30/170.64 (step @p98 :rule cong :premises (@p97 @p96) :args ((=> @t280 @t285))) % 170.30/170.64 (assume-push @p715 @t280) % 170.30/170.64 (step @p100 :rule skolemize :premises (@p90)) % 170.30/170.64 (step-pop @p716 :rule scope :premises (@p100)) % 170.30/170.64 (step @p101 :rule process_scope :premises (@p716) :args (@t285)) % 170.30/170.64 (step @p103 :rule eq_resolve :premises (@p101 @p98)) % 170.30/170.64 (step @p104 :rule implies_elim :premises (@p103)) % 170.30/170.64 (step @p105 :rule eq_resolve :premises (@p104 @p93)) % 170.30/170.64 (step @p106 :rule chain_m_resolution :premises (@p105 @p90) :args (@t283 @t250 (@list @t279))) % 170.30/170.64 (step @p107 :rule eq-symm :args (@t173 tptp.d_one)) % 170.30/170.64 (step @p108 :rule cong :premises (@p107) :args (@t175)) % 170.30/170.64 (step @p109 :rule and_elim :premises (@p1) :args (1)) % 170.30/170.64 (step @p110 :rule eq_resolve :premises (@p109 @p108)) % 170.30/170.64 (step @p111 :rule instantiate :premises (@p110) :args ((@list @t281))) % 170.30/170.64 (step @p112 :rule refl :args (@t286)) % 170.30/170.64 (step @p113 :rule refl :args (@t288)) % 170.30/170.64 (step @p114 :rule refl :args (@t289)) % 170.30/170.64 (step @p115 :rule bool-double-not-elim :args (@t261)) % 170.30/170.64 (step @p116 :rule refl :args (@t290)) % 170.30/170.64 (step @p117 :rule nary_cong :premises (@p116 @p115 @p114 @p113 @p112) :args ((or @t290 (not @t291) @t289 @t288 @t286))) % 170.30/170.64 (assume-push @p717 @t270) % 170.30/170.64 (assume-push @p718 @t283) % 170.30/170.64 (assume-push @p719 @t287) % 170.30/170.64 (assume-push @p720 @t275) % 170.30/170.64 (assume-push @p721 @t291) % 170.30/170.64 (step @p123 :rule evaluate :args (@t292)) % 170.30/170.64 (step @p124 :rule true_intro :premises (@p717)) % 170.30/170.64 (step @p125 :rule refl :args (@t205)) % 170.30/170.64 (step @p126 :rule refl :args (@t256)) % 170.30/170.64 (step @p127 :rule symm :premises (@p106)) % 170.30/170.64 (step @p128 :rule refl :args (@t197)) % 170.30/170.64 (step @p129 :rule cong :premises (@p128 @p111) :args (@t272)) % 170.30/170.64 (step @p130 :rule trans :premises (@p129 @p127)) % 170.30/170.64 (step @p131 :rule refl :args (@t227)) % 170.30/170.64 (step @p132 :rule cong :premises (@p131 @p130) :args (@t273)) % 170.30/170.64 (step @p133 :rule cong :premises (@p132 @p125) :args (@t274)) % 170.30/170.64 (step @p134 :rule refl :args (@t208)) % 170.30/170.64 (step @p135 :rule cong :premises (@p134 @p133) :args (@t293)) % 170.30/170.64 (step @p136 :rule cong :premises (@p134 @p78) :args (@t294)) % 170.30/170.64 (step @p137 :rule trans :premises (@p136 @p135)) % 170.30/170.64 (step @p138 :rule symm :premises (@p136)) % 170.30/170.64 (step @p139 :rule symm :premises (@p129)) % 170.30/170.64 (step @p140 :rule trans :premises (@p106 @p139 @p78)) % 170.30/170.64 (step @p141 :rule cong :premises (@p134 @p140) :args (@t258)) % 170.30/170.64 (step @p142 :rule trans :premises (@p141 @p138)) % 170.30/170.64 (step @p143 :rule trans :premises (@p142 @p137)) % 170.30/170.64 (step @p144 :rule cong :premises (@p143 @p126) :args (@t259)) % 170.30/170.64 (step @p145 :rule refl :args (@t254)) % 170.30/170.64 (step @p146 :rule cong :premises (@p145 @p144) :args (@t260)) % 170.30/170.64 (step @p147 :rule cong :premises (@p146 @p125) :args (@t261)) % 170.30/170.64 (step @p148 :rule false_intro :premises (@p721)) % 170.30/170.64 (step @p149 :rule symm :premises (@p148)) % 170.30/170.64 (step @p150 :rule trans :premises (@p149 @p147 @p124)) % 170.30/170.64 (step @p151 false :rule eq_resolve :premises (@p150 @p123)) % 170.30/170.64 (step-pop @p722 :rule scope :premises (@p151)) % 170.30/170.64 (step-pop @p723 :rule scope :premises (@p722)) % 170.30/170.64 (step-pop @p724 :rule scope :premises (@p723)) % 170.30/170.64 (step-pop @p725 :rule scope :premises (@p724)) % 170.30/170.64 (step-pop @p726 :rule scope :premises (@p725)) % 170.30/170.64 (step @p152 :rule process_scope :premises (@p726) :args (false)) % 170.30/170.64 (assume-push @p727 @t275) % 170.30/170.64 (assume-push @p728 @t291) % 170.30/170.64 (assume-push @p729 @t283) % 170.30/170.64 (assume-push @p730 @t287) % 170.30/170.64 (assume-push @p731 @t270) % 170.30/170.64 (step @p163 :rule and_intro :premises (@p731 @p106 @p111 @p78 @p728)) % 170.30/170.64 (step-pop @p732 :rule scope :premises (@p163)) % 170.30/170.64 (step-pop @p733 :rule scope :premises (@p732)) % 170.30/170.64 (step-pop @p734 :rule scope :premises (@p733)) % 170.30/170.64 (step-pop @p735 :rule scope :premises (@p734)) % 170.30/170.64 (step-pop @p736 :rule scope :premises (@p735)) % 170.30/170.64 (step @p164 :rule process_scope :premises (@p736) :args (@t295)) % 170.30/170.64 (step @p170 :rule implies_elim :premises (@p164)) % 170.30/170.64 (step @p171 :rule resolution :premises (@p170 @p152) :args (true @t295)) % 170.30/170.64 (step @p172 :rule not_and :premises (@p171)) % 170.30/170.64 (step @p173 :rule eq_resolve :premises (@p172 @p117)) % 170.30/170.64 (step @p174 :rule chain_m_resolution :premises (@p173 @p111 @p106 @p78 @p73 @p71 @p66 @p65 @p60 @p55) :args (@t269 (@list false false false false false true false false false) (@list @t287 @t283 @t275 @t270 @t271 @t261 @t262 @t264 @t255))) % 170.30/170.64 (step @p175 :rule refl :args (@t296)) % 170.30/170.64 (step @p176 :rule bool-double-not-elim :args (@t252)) % 170.30/170.64 (step @p177 :rule nary_cong :premises (@p176 @p175) :args ((or (not @t297) @t296))) % 170.30/170.64 (assume-push @p737 @t297) % 170.30/170.64 (step @p179 :rule skolemize :premises (@p737)) % 170.30/170.64 (step-pop @p738 :rule scope :premises (@p179)) % 170.30/170.64 (step @p180 :rule process_scope :premises (@p738) :args (@t296)) % 170.30/170.64 (step @p182 :rule implies_elim :premises (@p180)) % 170.30/170.64 (step @p183 :rule eq_resolve :premises (@p182 @p177)) % 170.30/170.64 (step @p184 :rule chain_m_resolution :premises (@p183 @p174) :args (@t252 @t243 (@list @t269))) % 170.30/170.64 (step @p185 :rule eq-symm :args (@t252 @t236)) % 170.30/170.64 (step @p186 :rule cong :premises (@p185) :args (@t298)) % 170.30/170.64 ; trust TRUST PREPROCESS_HO_ELIM % 170.30/170.64 (step @p187 :rule trust :premises () :args ((= (not (= @t316 (forall @t313 (or @t312 @t310 @t303 (not (_ @t2 @t299 @t207 @t299)) (not (_ @t2 @t299 @t206 @t299)) (_ @t2 @t299 @t300 @t299))))) @t298))) % 170.30/170.64 (step @p188 :rule refl :args (@t299)) % 170.30/170.64 (step @p189 :rule refl :args (@t96)) % 170.30/170.64 (step @p190 :rule cong :premises (@p189 @p188) :args ((= @t96 @t299))) % 170.30/170.64 (step @p191 :rule symm :premises (@p190)) % 170.30/170.64 (step @p192 :rule eq_resolve :premises (@p189 @p191)) % 170.30/170.64 (step @p193 :rule refl :args (@t300)) % 170.30/170.64 (step @p194 :rule cong :premises (@p192 @p193 @p192) :args (@t317)) % 170.30/170.64 (step @p195 :rule refl :args (@t206)) % 170.30/170.64 (step @p196 :rule cong :premises (@p192 @p195 @p192) :args (@t318)) % 170.30/170.64 (step @p197 :rule cong :premises (@p196) :args (@t319)) % 170.30/170.64 (step @p198 :rule refl :args (@t207)) % 170.30/170.64 (step @p199 :rule cong :premises (@p192 @p198 @p192) :args (@t320)) % 170.30/170.64 (step @p200 :rule cong :premises (@p199) :args (@t321)) % 170.30/170.64 (step @p201 :rule refl :args (@t303)) % 170.30/170.64 (step @p202 :rule refl :args (@t310)) % 170.30/170.64 (step @p203 :rule refl :args (@t312)) % 170.30/170.64 (step @p204 :rule nary_cong :premises (@p203 @p202 @p201 @p200 @p197 @p194) :args (@t322)) % 170.30/170.64 (step @p205 :rule cong :premises (@p204) :args ((forall @t313 @t322))) % 170.30/170.64 (step @p206 :rule refl :args (@t317)) % 170.30/170.64 (step @p207 :rule refl :args (@t319)) % 170.30/170.64 (step @p208 :rule refl :args (@t321)) % 170.30/170.64 (step @p209 :rule refl :args (@t24)) % 170.30/170.64 (step @p210 :rule refl :args (@t8)) % 170.30/170.64 (step @p211 :rule cong :premises (@p192 @p210 @p192 @p209) :args (@t323)) % 170.30/170.64 (step @p212 :rule cong :premises (@p192 @p211 @p192) :args (@t324)) % 170.30/170.64 (step @p213 :rule cong :premises (@p192 @p209 @p192) :args (@t325)) % 170.30/170.64 (step @p214 :rule cong :premises (@p213) :args (@t326)) % 170.30/170.64 (step @p215 :rule cong :premises (@p192 @p210 @p192) :args (@t327)) % 170.30/170.64 (step @p216 :rule cong :premises (@p215) :args (@t328)) % 170.30/170.64 (step @p217 :rule nary_cong :premises (@p216 @p214 @p212) :args (@t329)) % 170.30/170.64 (step @p218 :rule cong :premises (@p217) :args (@t330)) % 170.30/170.64 (step @p219 :rule cong :premises (@p218) :args (@t331)) % 170.30/170.64 (step @p220 :rule refl :args (@t310)) % 170.30/170.64 (step @p221 :rule refl :args (@t312)) % 170.30/170.64 (step @p222 :rule nary_cong :premises (@p221 @p220 @p219 @p208 @p207 @p206) :args (@t332)) % 170.30/170.64 (step @p223 :rule cong :premises (@p222) :args (@t333)) % 170.30/170.64 (step @p224 :rule trans :premises (@p223 @p205)) % 170.30/170.64 (step @p225 :rule refl :args (@t316)) % 170.30/170.64 (step @p226 :rule cong :premises (@p225 @p224) :args (@t334)) % 170.30/170.64 (step @p227 :rule cong :premises (@p226) :args ((not @t334))) % 170.30/170.64 (step @p228 :rule and_elim :premises (@p1) :args (10)) % 170.30/170.64 (step @p229 :rule refl :args (@t300)) % 170.30/170.64 (step @p230 :rule cong :premises (@p228 @p229 @p228) :args (@t335)) % 170.30/170.64 (step @p231 :rule refl :args (@t206)) % 170.30/170.64 (step @p232 :rule cong :premises (@p228 @p231 @p228) :args (@t336)) % 170.30/170.64 (step @p233 :rule cong :premises (@p232) :args (@t337)) % 170.30/170.64 (step @p234 :rule refl :args (@t207)) % 170.30/170.64 (step @p235 :rule cong :premises (@p228 @p234 @p228) :args (@t338)) % 170.30/170.64 (step @p236 :rule cong :premises (@p235) :args (@t339)) % 170.30/170.64 (step @p237 :rule refl :args (@t24)) % 170.30/170.64 (step @p238 :rule refl :args (@t8)) % 170.30/170.64 (step @p239 :rule cong :premises (@p228 @p238 @p228 @p237) :args (@t340)) % 170.30/170.64 (step @p240 :rule cong :premises (@p228 @p239 @p228) :args (@t341)) % 170.30/170.64 (step @p241 :rule cong :premises (@p228 @p237 @p228) :args (@t342)) % 170.30/170.64 (step @p242 :rule cong :premises (@p241) :args (@t343)) % 170.30/170.64 (step @p243 :rule cong :premises (@p228 @p238 @p228) :args (@t344)) % 170.30/170.64 (step @p244 :rule cong :premises (@p243) :args (@t345)) % 170.30/170.64 (step @p245 :rule nary_cong :premises (@p244 @p242 @p240) :args (@t346)) % 170.30/170.64 (step @p246 :rule cong :premises (@p245) :args (@t347)) % 170.30/170.64 (step @p247 :rule cong :premises (@p246) :args (@t348)) % 170.30/170.64 (step @p248 :rule nary_cong :premises (@p221 @p220 @p247 @p236 @p233 @p230) :args (@t349)) % 170.30/170.64 (step @p249 :rule cong :premises (@p248) :args (@t350)) % 170.30/170.64 (step @p250 :rule refl :args (@t314)) % 170.30/170.64 (step @p251 :rule cong :premises (@p192 @p250 @p192) :args (@t351)) % 170.30/170.64 (step @p252 :rule refl :args (@t139)) % 170.30/170.64 (step @p253 :rule cong :premises (@p192 @p252 @p192) :args (@t352)) % 170.30/170.64 (step @p254 :rule cong :premises (@p253) :args (@t353)) % 170.30/170.64 (step @p255 :rule refl :args (@t140)) % 170.30/170.64 (step @p256 :rule cong :premises (@p192 @p255 @p192) :args (@t354)) % 170.30/170.64 (step @p257 :rule cong :premises (@p256) :args (@t355)) % 170.30/170.64 (step @p258 :rule refl :args (@t315)) % 170.30/170.64 (step @p259 :rule nary_cong :premises (@p203 @p202 @p258 @p257 @p254 @p251) :args (@t356)) % 170.30/170.64 (step @p260 :rule cong :premises (@p259) :args ((forall @t148 @t356))) % 170.30/170.64 (step @p261 :rule refl :args (@t351)) % 170.30/170.64 (step @p262 :rule refl :args (@t353)) % 170.30/170.64 (step @p263 :rule refl :args (@t355)) % 170.30/170.64 (step @p264 :rule cong :premises (@p210 @p192) :args (@t357)) % 170.30/170.64 (step @p265 :rule cong :premises (@p264 @p209) :args (@t358)) % 170.30/170.64 (step @p266 :rule cong :premises (@p192 @p265 @p192) :args (@t359)) % 170.30/170.64 (step @p267 :rule nary_cong :premises (@p216 @p214 @p266) :args (@t360)) % 170.30/170.64 (step @p268 :rule cong :premises (@p267) :args (@t361)) % 170.30/170.64 (step @p269 :rule cong :premises (@p268) :args (@t362)) % 170.30/170.64 (step @p270 :rule nary_cong :premises (@p221 @p220 @p269 @p263 @p262 @p261) :args (@t363)) % 170.30/170.64 (step @p271 :rule cong :premises (@p270) :args (@t364)) % 170.30/170.64 (step @p272 :rule trans :premises (@p271 @p260)) % 170.30/170.64 (step @p273 :rule refl :args (tptp.hoasinduction_lem2)) % 170.30/170.64 (step @p274 :rule cong :premises (@p273 @p272) :args ((= tptp.hoasinduction_lem2 @t364))) % 170.30/170.64 (step @p275 :rule refl :args (@t314)) % 170.30/170.64 (step @p276 :rule cong :premises (@p228 @p275 @p228) :args (@t365)) % 170.30/170.64 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:rule refl :args (@t340)) % 170.30/170.64 (step @p491 :rule cong :premises (@p294 @p490 @p294) :args (@t341)) % 170.30/170.64 (step @p492 :rule trans :premises (@p491 @p489)) % 170.30/170.64 (step @p493 :rule ho_cong :premises (@p298 @p490)) % 170.30/170.64 (step @p494 :rule ho_cong :premises (@p493 @p294)) % 170.30/170.64 (step @p495 :rule cong :premises (@p494 @p492) :args ((= (_ (_ @t3 @t340) tptp.id) @t341))) % 170.30/170.64 (step @p496 :rule symm :premises (@p495)) % 170.30/170.64 (step @p497 :rule refl :args (@t186)) % 170.30/170.64 (step @p498 :rule eq_resolve :premises (@p497 @p496)) % 170.30/170.64 (step @p499 :rule refl :args (@t185)) % 170.30/170.64 (step @p500 :rule cong :premises (@p499 @p490) :args ((= @t185 @t340))) % 170.30/170.64 (step @p501 :rule symm :premises (@p500)) % 170.30/170.64 (step @p502 :rule eq_resolve :premises (@p499 @p501)) % 170.30/170.64 (step @p503 :rule ho_cong :premises (@p298 @p502)) % 170.30/170.64 (step @p504 :rule ho_cong :premises (@p503 @p294)) % 170.30/170.64 (step @p505 :rule trans :premises (@p504 @p498)) % 170.30/170.64 (step @p506 :rule nary_cong :premises (@p371 @p365 @p505) :args (@t395)) % 170.30/170.64 (step @p507 :rule cong :premises (@p506) :args ((forall @t32 @t395))) % 170.30/170.64 (step @p508 :rule aci_norm :args ((= (or @t10 (or @t30 @t186)) @t395))) % 170.30/170.64 (step @p509 :rule bool-impl-elim :args (@t29 @t186)) % 170.30/170.64 (step @p510 :rule nary_cong :premises (@p482 @p509) :args ((or @t10 @t187))) % 170.30/170.64 (step @p511 :rule trans :premises (@p510 @p508)) % 170.30/170.64 (step @p512 :rule bool-impl-elim :args (@t9 @t187)) % 170.30/170.64 (step @p513 :rule trans :premises (@p512 @p511)) % 170.30/170.64 (step @p514 :rule cong :premises (@p513) :args (@t188)) % 170.30/170.64 (step @p515 :rule trans :premises (@p514 @p507)) % 170.30/170.64 (step @p516 :rule cong :premises (@p515 @p488) :args (@t189)) % 170.30/170.64 (step @p517 :rule bool-impl-elim :args (@t41 @t38)) % 170.30/170.64 (step @p518 :rule cong :premises (@p517) :args (@t190)) % 170.30/170.64 (step @p519 :rule trans :premises (@p518 @p420)) % 170.30/170.64 (step @p520 :rule cong :premises (@p519 @p516) :args (@t191)) % 170.30/170.64 (step @p521 :rule bool-impl-elim :args (@t38 @t41)) % 170.30/170.64 (step @p522 :rule cong :premises (@p521) :args (@t192)) % 170.30/170.64 (step @p523 :rule trans :premises (@p522 @p424)) % 170.30/170.64 (step @p524 :rule cong :premises (@p523 @p520) :args (@t193)) % 170.30/170.64 (step @p525 :rule cong :premises (@p524) :args (@t194)) % 170.30/170.64 (step @p526 :rule trans :premises (@p525 @p460)) % 170.30/170.64 (step @p527 :rule cong :premises (@p273 @p526) :args (@t195)) % 170.30/170.64 (step @p528 :rule cong :premises (@p527) :args (@t196)) % 170.30/170.64 (step @p529 :rule trans :premises (@p528 @p435 @p187 @p186)) % 170.30/170.64 (step @p530 :rule eq_resolve :premises (@p2 @p529)) % 170.30/170.64 (step @p531 :rule not_equiv_elim2 :premises (@p530)) % 170.30/170.64 (step @p532 :rule chain_m_resolution :premises (@p531 @p184) :args (@t396 @t243 (@list @t252))) % 170.30/170.64 (step @p533 :rule refl :args (@t413)) % 170.30/170.64 (step @p534 :rule bool-double-not-elim :args (@t236)) % 170.30/170.64 (step @p535 :rule nary_cong :premises (@p534 @p533) :args ((or (not @t396) @t413))) % 170.30/170.64 (assume-push @p739 @t396) % 170.30/170.64 (step @p537 :rule skolemize :premises (@p739)) % 170.30/170.64 (step-pop @p740 :rule scope :premises (@p537)) % 170.30/170.64 (step @p538 :rule process_scope :premises (@p740) :args (@t413)) % 170.30/170.64 (step @p540 :rule implies_elim :premises (@p538)) % 170.30/170.64 (step @p541 :rule eq_resolve :premises (@p540 @p535)) % 170.30/170.64 (step @p542 :rule chain_m_resolution :premises (@p541 @p532) :args (@t413 @t250 (@list @t236))) % 170.30/170.64 (step @p543 :rule bool-double-not-elim :args (@t408)) % 170.30/170.64 (step @p544 :rule refl :args (@t412)) % 170.30/170.64 (step @p545 :rule nary_cong :premises (@p544 @p543) :args ((or @t412 (not @t409)))) % 170.30/170.64 (step @p546 :rule cnf_or_neg :args (@t412 2)) % 170.30/170.64 (step @p547 :rule eq_resolve :premises (@p546 @p545)) % 170.30/170.64 (step @p548 :rule reordering :premises (@p547) :args ((or @t408 @t412))) % 170.30/170.64 (step @p549 :rule chain_m_resolution :premises (@p548 @p542) :args (@t408 @t250 @t414)) % 170.30/170.64 (assume-push @p741 @t408) % 170.30/170.64 (step @p551 :rule instantiate :premises (@p741) :args ((@list @t237 @t397))) % 170.30/170.64 (step-pop @p742 :rule scope :premises (@p551)) % 170.30/170.64 (step @p552 :rule process_scope :premises (@p742) :args (@t416)) % 170.30/170.64 (step @p554 :rule implies_elim :premises (@p552)) % 170.30/170.64 (step @p555 :rule chain_m_resolution :premises (@p554 @p549) :args (@t416 @t243 (@list @t408))) % 170.30/170.64 (step @p556 :rule bool-double-not-elim :args (@t404)) % 170.30/170.64 (step @p557 :rule nary_cong :premises (@p544 @p556) :args ((or @t412 (not @t405)))) % 170.30/170.64 (step @p558 :rule cnf_or_neg :args (@t412 4)) % 170.30/170.64 (step @p559 :rule eq_resolve :premises (@p558 @p557)) % 170.30/170.64 (step @p560 :rule reordering :premises (@p559) :args ((or @t404 @t412))) % 170.30/170.64 (step @p561 :rule chain_m_resolution :premises (@p560 @p542) :args (@t404 @t250 @t414)) % 170.30/170.64 (step @p562 :rule bool-double-not-elim :args (@t406)) % 170.30/170.64 (step @p563 :rule nary_cong :premises (@p544 @p562) :args ((or @t412 (not @t407)))) % 170.30/170.64 (step @p564 :rule cnf_or_neg :args (@t412 3)) % 170.30/170.64 (step @p565 :rule eq_resolve :premises (@p564 @p563)) % 170.30/170.64 (step @p566 :rule reordering :premises (@p565) :args ((or @t406 @t412))) % 170.30/170.64 (step @p567 :rule chain_m_resolution :premises (@p566 @p542) :args (@t406 @t250 @t414)) % 170.30/170.64 (step @p568 :rule cnf_or_pos :args (@t416)) % 170.30/170.64 (step @p569 :rule reordering :premises (@p568) :args ((or @t407 @t405 @t415 (not @t416)))) % 170.30/170.64 (step @p570 :rule chain_m_resolution :premises (@p569 @p567 @p561 @p555) :args (@t415 (@list false false false) (@list @t406 @t404 @t416))) % 170.30/170.64 (step @p571 :rule cnf_or_neg :args (@t412 5)) % 170.30/170.64 (step @p572 :rule chain_m_resolution :premises (@p571 @p542) :args (@t417 @t250 @t414)) % 170.30/170.64 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.30/170.64 (step @p573 :rule trust :premises () :args ((forall (@list @t419 @t418) (or (not (forall @t421 (= (_ @t210 @t419 @t420) (_ @t210 @t418 @t420)))) (= @t419 @t418))))) % 170.30/170.64 (step @p574 :rule instantiate :premises (@p573) :args ((@list @t294 @t423))) % 170.30/170.64 (step @p575 :rule eq-symm :args (@t425 @t199)) % 170.30/170.64 (step @p576 :rule cong :premises (@p575) :args (@t426)) % 170.30/170.64 (step @p577 :rule cong :premises (@p576) :args (@t427)) % 170.30/170.64 (step @p578 :rule cong :premises (@p577) :args (@t428)) % 170.30/170.64 (step @p579 :rule cong :premises (@p25 @p578) :args ((=> @t200 @t428))) % 170.30/170.64 (assume-push @p743 @t200) % 170.30/170.64 (step @p581 :rule instantiate :premises (@p20) :args ((@list @t425))) % 170.30/170.64 (step-pop @p744 :rule scope :premises (@p581)) % 170.30/170.64 (step @p582 :rule process_scope :premises (@p744) :args (@t428)) % 170.30/170.64 (step @p584 :rule eq_resolve :premises (@p582 @p579)) % 170.30/170.64 (step @p585 :rule implies_elim :premises (@p584)) % 170.30/170.64 (step @p586 :rule chain_m_resolution :premises (@p585 @p20) :args (@t430 @t243 @t244)) % 170.30/170.64 (step @p587 :rule refl :args (@t433)) % 170.30/170.64 (step @p588 :rule bool-double-not-elim :args (@t429)) % 170.30/170.64 (step @p589 :rule nary_cong :premises (@p588 @p587) :args ((or (not @t430) @t433))) % 170.30/170.64 (step @p590 :rule eq-symm :args (@t432 @t425)) % 170.30/170.64 (step @p591 :rule bool-double-not-elim :args (@t434)) % 170.30/170.64 (step @p592 :rule trans :premises (@p591 @p590)) % 170.30/170.64 (step @p593 :rule refl :args (@t430)) % 170.30/170.64 (step @p594 :rule cong :premises (@p593 @p592) :args ((=> @t430 @t435))) % 170.30/170.64 (assume-push @p745 @t430) % 170.30/170.64 (step @p596 :rule skolemize :premises (@p586)) % 170.30/170.64 (step-pop @p746 :rule scope :premises (@p596)) % 170.30/170.64 (step @p597 :rule process_scope :premises (@p746) :args (@t435)) % 170.30/170.64 (step @p599 :rule eq_resolve :premises (@p597 @p594)) % 170.30/170.64 (step @p600 :rule implies_elim :premises (@p599)) % 170.30/170.64 (step @p601 :rule eq_resolve :premises (@p600 @p589)) % 170.30/170.64 (step @p602 :rule chain_m_resolution :premises (@p601 @p586) :args (@t433 @t250 (@list @t429))) % 170.30/170.64 (step @p603 :rule symm :premises (@p602)) % 170.30/170.64 (step @p604 :rule instantiate :premises (@p110) :args ((@list @t431))) % 170.30/170.64 (step @p128 :rule refl :args (@t197)) % 170.30/170.64 (step @p605 :rule cong :premises (@p128 @p604) :args (@t272)) % 170.30/170.64 (step @p606 :rule trans :premises (@p605 @p603)) % 170.30/170.64 (step @p607 :rule refl :args (@t423)) % 170.30/170.64 (step @p608 :rule cong :premises (@p607 @p606) :args (@t436)) % 170.30/170.64 ; trust TRUST PREPROCESS_HO_ELIM % 170.30/170.64 (step @p609 :rule trust :premises () :args ((= (= @t97 @t163) (= @t272 @t436)))) % 170.30/170.64 (step @p610 :rule eq-symm :args (@t163 @t97)) % 170.30/170.64 (step @p611 :rule trans :premises (@p610 @p609)) % 170.30/170.64 (step @p612 :rule and_elim :premises (@p1) :args (14)) % 170.30/170.64 (step @p613 :rule eq_resolve :premises (@p612 @p611)) % 170.30/170.64 ; trust TRUST PREPROCESS_HO_ELIM % 170.30/170.64 (step @p614 :rule trust :premises () :args ((= (= @t97 @t165) (= @t272 (_ @t210 @t294 @t272))))) % 170.30/170.64 (step @p615 :rule eq-symm :args (@t165 @t97)) % 170.30/170.64 (step @p616 :rule trans :premises (@p615 @p614)) % 170.30/170.64 (step @p617 :rule and_elim :premises (@p1) :args (7)) % 170.30/170.64 (step @p618 :rule eq_resolve :premises (@p617 @p616)) % 170.30/170.64 (step @p619 :rule symm :premises (@p618)) % 170.30/170.64 (step @p620 :rule refl :args (@t272)) % 170.30/170.64 (step @p134 :rule refl :args (@t208)) % 170.30/170.64 (step @p136 :rule cong :premises (@p134 @p78) :args (@t294)) % 170.30/170.64 (step @p138 :rule symm :premises (@p136)) % 170.30/170.64 (step @p621 :rule cong :premises (@p138 @p620) :args ((_ @t210 @t293 @t272))) % 170.30/170.64 (step @p622 :rule symm :premises (@p606)) % 170.30/170.64 (step @p623 :rule cong :premises (@p136 @p622) :args (@t437)) % 170.30/170.64 (step @p624 :rule trans :premises (@p623 @p621 @p619 @p613 @p608)) % 170.30/170.64 (step @p625 :rule refl :args (@t439)) % 170.30/170.64 (step @p626 :rule bool-double-not-elim :args (@t424)) % 170.30/170.64 (step @p627 :rule nary_cong :premises (@p626 @p625) :args ((or (not @t440) @t439))) % 170.30/170.64 (assume-push @p747 @t440) % 170.30/170.64 (step @p629 :rule skolemize :premises (@p747)) % 170.30/170.64 (step-pop @p748 :rule scope :premises (@p629)) % 170.30/170.64 (step @p630 :rule process_scope :premises (@p748) :args (@t439)) % 170.30/170.64 (step @p632 :rule implies_elim :premises (@p630)) % 170.30/170.64 (step @p633 :rule eq_resolve :premises (@p632 @p627)) % 170.30/170.64 (step @p634 :rule chain_m_resolution :premises (@p633 @p624) :args (@t424 @t243 (@list @t438))) % 170.30/170.64 (step @p635 :rule cnf_or_pos :args (@t442)) % 170.30/170.64 (step @p636 :rule reordering :premises (@p635) :args ((or @t440 @t441 (not @t442)))) % 170.30/170.64 (step @p637 :rule chain_m_resolution :premises (@p636 @p634 @p574) :args (@t441 (@list false false) (@list @t424 @t442))) % 170.30/170.64 (step @p638 :rule refl :args (@t443)) % 170.30/170.64 (step @p639 :rule refl :args (@t445)) % 170.30/170.64 (step @p640 :rule bool-double-not-elim :args (@t403)) % 170.30/170.64 (step @p641 :rule refl :args (@t446)) % 170.30/170.64 (step @p642 :rule nary_cong :premises (@p116 @p641 @p640 @p639 @p638) :args ((or @t290 @t446 (not @t417) @t445 @t443))) % 170.30/170.64 (assume-push @p749 @t415) % 170.30/170.64 (assume-push @p750 @t444) % 170.30/170.64 (assume-push @p751 @t441) % 170.30/170.64 (assume-push @p752 @t275) % 170.30/170.64 (assume-push @p753 @t417) % 170.30/170.64 (step @p123 :rule evaluate :args (@t292)) % 170.30/170.64 (step @p648 :rule true_intro :premises (@p749)) % 170.30/170.64 (step @p125 :rule refl :args (@t205)) % 170.30/170.64 (step @p649 :rule refl :args (@t397)) % 170.30/170.64 (step @p650 :rule symm :premises (@p49)) % 170.30/170.64 (step @p651 :rule instantiate :premises (@p110) :args (@t447)) % 170.30/170.64 (step @p652 :rule cong :premises (@p128 @p651) :args (@t272)) % 170.30/170.64 (step @p653 :rule trans :premises (@p652 @p650)) % 170.30/170.64 (step @p654 :rule refl :args (@t216)) % 170.30/170.64 (step @p655 :rule cong :premises (@p654 @p653) :args (@t422)) % 170.30/170.64 (step @p656 :rule cong :premises (@p655 @p125) :args (@t423)) % 170.30/170.64 (step @p657 :rule trans :premises (@p751 @p656)) % 170.30/170.64 (step @p658 :rule trans :premises (@p652 @p650)) % 170.30/170.64 (step @p659 :rule symm :premises (@p658)) % 170.30/170.64 (step @p660 :rule trans :premises (@p659 @p78)) % 170.30/170.64 (step @p661 :rule cong :premises (@p134 @p660) :args (@t398)) % 170.30/170.64 (step @p662 :rule trans :premises (@p661 @p138)) % 170.30/170.64 (step @p663 :rule trans :premises (@p662 @p657)) % 170.30/170.64 (step @p664 :rule cong :premises (@p663 @p649) :args (@t399)) % 170.30/170.64 (step @p665 :rule refl :args (@t401)) % 170.30/170.64 (step @p666 :rule cong :premises (@p665 @p664) :args (@t402)) % 170.30/170.64 (step @p667 :rule cong :premises (@p666 @p125) :args (@t403)) % 170.30/170.64 (step @p668 :rule false_intro :premises (@p753)) % 170.30/170.64 (step @p669 :rule symm :premises (@p668)) % 170.30/170.64 (step @p670 :rule trans :premises (@p669 @p667 @p648)) % 170.30/170.64 (step @p671 false :rule eq_resolve :premises (@p670 @p123)) % 170.30/170.64 (step-pop @p754 :rule scope :premises (@p671)) % 170.30/170.64 (step-pop @p755 :rule scope :premises (@p754)) % 170.30/170.64 (step-pop @p756 :rule scope :premises (@p755)) % 170.30/170.64 (step-pop @p757 :rule scope :premises (@p756)) % 170.30/170.64 (step-pop @p758 :rule scope :premises (@p757)) % 170.30/170.64 (step @p672 :rule process_scope :premises (@p758) :args (false)) % 170.30/170.64 (assume-push @p759 @t275) % 170.30/170.64 (assume-push @p760 @t441) % 170.30/170.64 (assume-push @p761 @t417) % 170.30/170.64 (assume-push @p762 @t444) % 170.30/170.64 (assume-push @p763 @t415) % 170.30/170.64 (step @p650 :rule symm :premises (@p49)) % 170.30/170.64 (step @p651 :rule instantiate :premises (@p110) :args (@t447)) % 170.30/170.64 (step @p652 :rule cong :premises (@p128 @p651) :args (@t272)) % 170.30/170.64 (step @p683 :rule trans :premises (@p652 @p650)) % 170.30/170.64 (step @p684 :rule and_intro :premises (@p763 @p683 @p760 @p78 @p761)) % 170.30/170.64 (step-pop @p764 :rule scope :premises (@p684)) % 170.30/170.64 (step-pop @p765 :rule scope :premises (@p764)) % 170.30/170.64 (step-pop @p766 :rule scope :premises (@p765)) % 170.30/170.64 (step-pop @p767 :rule scope :premises (@p766)) % 170.30/170.64 (step-pop @p768 :rule scope :premises (@p767)) % 170.30/170.64 (step @p685 :rule process_scope :premises (@p768) :args (@t448)) % 170.30/170.64 (step @p691 :rule implies_elim :premises (@p685)) % 170.30/170.64 (step @p692 :rule resolution :premises (@p691 @p672) :args (true @t448)) % 170.30/170.64 (step @p693 :rule not_and :premises (@p692)) % 170.30/170.64 (step @p694 :rule eq_resolve :premises (@p693 @p642)) % 170.30/170.64 (step @p695 :rule chain_m_resolution :premises (@p694 @p78 @p637 @p572 @p570) :args (@t445 (@list false false true false) (@list @t275 @t441 @t403 @t415))) % 170.30/170.64 (step @p651 :rule instantiate :premises (@p110) :args (@t447)) % 170.30/170.64 (assume-push @p769 @t247) % 170.30/170.64 (assume-push @p770 @t449) % 170.30/170.64 (step @p650 :rule symm :premises (@p49)) % 170.30/170.64 (step @p652 :rule cong :premises (@p128 @p651) :args (@t272)) % 170.30/170.64 (step @p698 :rule trans :premises (@p652 @p650)) % 170.30/170.64 (step-pop @p771 :rule scope :premises (@p698)) % 170.30/170.64 (step-pop @p772 :rule scope :premises (@p771)) % 170.30/170.64 (step @p699 :rule process_scope :premises (@p772) :args (@t444)) % 170.30/170.64 (step @p702 :rule implies_elim :premises (@p699)) % 170.30/170.64 (step @p703 :rule cnf_and_neg :args (@t450)) % 170.30/170.64 (step @p704 :rule resolution :premises (@p703 @p702) :args (true @t450)) % 170.30/170.64 (step @p705 :rule reordering :premises (@p704) :args ((or @t444 (not @t247) (not @t449)))) % 170.30/170.64 (step @p706 false :rule chain_m_resolution :premises (@p705 @p651 @p695 @p49) :args (false (@list false true false) (@list @t449 @t444 @t247))) % 170.30/170.64 ) % 170.30/170.64 % SZS output end Proof % 170.30/170.64 % cvc5 exiting %------------------------------------------------------------------------------