%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 123.27s 123.50s % Output : Proof 123.27s % 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. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n017.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 23:00:46 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.55 %----Proving TH0 % 123.27/123.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 123.27/123.50 --- 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... % 123.27/123.50 --- 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... % 123.27/123.50 % SZS status Theorem % 123.27/123.50 % SZS output start Proof % 123.27/123.50 ( % 123.27/123.50 (declare-sort tptp.term 0) % 123.27/123.50 (declare-sort tptp.subst 0) % 123.27/123.50 (declare-sort tptp.d_term 0) % 123.27/123.50 (declare-sort tptp.d_subst 0) % 123.27/123.50 (declare-const tptp.hoasap (-> tptp.subst tptp.term tptp.subst tptp.term tptp.term)) % 123.27/123.50 (declare-const tptp.hoaslam (-> tptp.subst (-> tptp.subst tptp.term tptp.term) tptp.term)) % 123.27/123.50 (declare-const tptp.hoasinduction_p_and_p_prime (-> (-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool) Bool)) % 123.27/123.50 (declare-const tptp.pushprop_lem1v2 Bool) % 123.27/123.50 (declare-const tptp.pushprop_lem1_gthm Bool) % 123.27/123.50 (declare-const tptp.axmap Bool) % 123.27/123.50 (declare-const tptp.pushprop_lem0_gthm Bool) % 123.27/123.50 (declare-const tptp.shinj Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem1v2 Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 123.27/123.50 (declare-const tptp.induction2lem Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 123.27/123.50 (declare-const tptp.axvarshift Bool) % 123.27/123.50 (declare-const tptp.hoasapinj2 Bool) % 123.27/123.50 (declare-const tptp.hoasapnotvar_gthm Bool) % 123.27/123.50 (declare-const tptp.hoasapinj1 Bool) % 123.27/123.50 (declare-const tptp.ulamvar1 Bool) % 123.27/123.50 (declare-const tptp.induction2lem_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 123.27/123.50 (declare-const tptp.apnotvar Bool) % 123.27/123.50 (declare-const tptp.pushprop_lthm_orig Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 123.27/123.50 (declare-const tptp.hoaslaminj Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3aaa Bool) % 123.27/123.50 (declare-const tptp.induction2lem_gthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3 Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem2 Bool) % 123.27/123.50 (declare-const tptp.termmset_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem1 Bool) % 123.27/123.50 (declare-const tptp.hoaslamnotap_lthm Bool) % 123.27/123.50 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasapnotvar Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem0 Bool) % 123.27/123.50 (declare-const tptp.hoasinduction Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_gthm Bool) % 123.27/123.50 (declare-const tptp.axapp Bool) % 123.27/123.50 (declare-const tptp.hoaslamnotvar_lthm Bool) % 123.27/123.50 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 123.27/123.50 (declare-const tptp.ulamvarind Bool) % 123.27/123.50 (declare-const tptp.induction Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 123.27/123.50 (declare-const tptp.termmset_gthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3aa Bool) % 123.27/123.50 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 123.27/123.50 (declare-const tptp.hoaslamnotap_gthm Bool) % 123.27/123.50 (declare-const tptp.hoaslamnotvar_gthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 123.27/123.50 (declare-const tptp.pushprop_lem2v2 Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 123.27/123.50 (declare-const tptp.axclos Bool) % 123.27/123.50 (declare-const tptp.axassoc Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem2v2 Bool) % 123.27/123.50 (declare-const tptp.pushprop_lthm Bool) % 123.27/123.50 (declare-const tptp.apinj2 Bool) % 123.27/123.50 (declare-const tptp.apinj1 Bool) % 123.27/123.50 (declare-const tptp.hoasapinj2_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3v2a Bool) % 123.27/123.50 (declare-const tptp.hoasapinj1_lthm Bool) % 123.27/123.50 (declare-const tptp.hoaslaminj_lthm Bool) % 123.27/123.50 (declare-const tptp.axvarcons Bool) % 123.27/123.50 (declare-const tptp.axscons Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 123.27/123.50 (declare-const tptp.d_one tptp.d_term) % 123.27/123.50 (declare-const tptp.hoaslamnotap Bool) % 123.27/123.50 (declare-const tptp.ulamvarsh Bool) % 123.27/123.50 (declare-const tptp.pushprop_lem3v2 Bool) % 123.27/123.50 (declare-const tptp.axshiftcons Bool) % 123.27/123.50 (declare-const tptp.id tptp.subst) % 123.27/123.50 (declare-const tptp.pushprop_lem1_lthm Bool) % 123.27/123.50 (declare-const tptp.hoasvar (-> tptp.subst tptp.term tptp.subst Bool)) % 123.27/123.50 (declare-const tptp.pushprop_lem0_lthm Bool) % 123.27/123.50 (declare-const tptp.one tptp.term) % 123.27/123.50 (declare-const tptp.substmonoid_gthm Bool) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3v2 Bool) % 123.27/123.50 (declare-const tptp.sh tptp.subst) % 123.27/123.50 (declare-const tptp.termmset Bool) % 123.27/123.50 (declare-const tptp.induction2 Bool) % 123.27/123.50 (declare-const tptp.pushprop_p_and_p_prime (-> tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool) Bool)) % 123.27/123.50 (declare-const tptp.lam (-> tptp.term tptp.term)) % 123.27/123.50 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 123.27/123.50 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 123.27/123.50 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 123.27/123.50 (declare-const tptp.axvarid Bool) % 123.27/123.50 (declare-const tptp.d_id tptp.d_subst) % 123.27/123.50 (declare-const tptp.var (-> tptp.term Bool)) % 123.27/123.50 (declare-const tptp.d2term (-> tptp.d_term tptp.term)) % 123.27/123.50 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 123.27/123.50 (declare-const tptp.hoasapnotvar_lthm Bool) % 123.27/123.50 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 123.27/123.50 (declare-const tptp.hoasinduction_lthm_3 Bool) % 123.27/123.50 (declare-const tptp.d2subst (-> tptp.d_subst tptp.subst)) % 123.27/123.50 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 123.27/123.51 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 123.27/123.51 (declare-const tptp.induction2_gthm Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem3a Bool) % 123.27/123.51 (declare-const tptp.lamnotvar Bool) % 123.27/123.51 (declare-const tptp.substmonoid Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem3b Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 123.27/123.51 (declare-const tptp.pushprop Bool) % 123.27/123.51 (declare-const tptp.substmonoid_lthm Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 123.27/123.51 (declare-const tptp.induction2_lthm Bool) % 123.27/123.51 (declare-const tptp.hoaslaminj_gthm Bool) % 123.27/123.51 (declare-const tptp.axidl Bool) % 123.27/123.51 (declare-const tptp.hoaslamnotvar Bool) % 123.27/123.51 (declare-const tptp.hoasapinj1_gthm Bool) % 123.27/123.51 (declare-const tptp.lamnotap Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 123.27/123.51 (declare-const tptp.hoasapinj2_gthm Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 123.27/123.51 (declare-const tptp.axabs Bool) % 123.27/123.51 (declare-const tptp.pushprop_gthm Bool) % 123.27/123.51 (declare-const tptp.pushprop_lem0 Bool) % 123.27/123.51 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 123.27/123.51 (declare-const tptp.laminj Bool) % 123.27/123.51 (declare-const tptp.pushprop_lem1 Bool) % 123.27/123.51 (declare-const tptp.axidr Bool) % 123.27/123.51 (define @t1 () (@var "Bound_variable_3283" tptp.term)) % 123.27/123.51 (define @t2 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 123.27/123.51 (define @t3 () (_ @t2 tptp.id)) % 123.27/123.51 (define @t4 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 123.27/123.51 (define @t5 () (_ (_ @t4 tptp.sh) tptp.one)) % 123.27/123.51 (define @t6 () (_ tptp.lam @t5)) % 123.27/123.51 (define @t7 () (_ (_ @t3 @t6) tptp.id)) % 123.27/123.51 (define @t8 () (@var "A" tptp.term)) % 123.27/123.51 (define @t9 () (_ (_ @t3 @t8) tptp.id)) % 123.27/123.51 (define @t10 () (not @t9)) % 123.27/123.51 (define @t11 () (@list @t8)) % 123.27/123.51 (define @t12 () (not (forall @t11 (or @t10 (_ (_ @t3 (_ (_ @t4 tptp.id) @t8)) tptp.id))))) % 123.27/123.51 (define @t13 () (@var "N" tptp.subst)) % 123.27/123.51 (define @t14 () (_ tptp.sub @t8)) % 123.27/123.51 (define @t15 () (_ @t14 @t13)) % 123.27/123.51 (define @t16 () (@var "M" tptp.subst)) % 123.27/123.51 (define @t17 () (_ tptp.comp @t16)) % 123.27/123.51 (define @t18 () (_ @t17 @t13)) % 123.27/123.51 (define @t19 () (_ (_ @t4 @t16) @t8)) % 123.27/123.51 (define @t20 () (@list @t16 @t8 @t13)) % 123.27/123.51 (define @t21 () (not (forall @t20 (= (_ (_ tptp.sub @t19) @t13) (_ (_ @t4 @t18) @t15))))) % 123.27/123.51 (define @t22 () (@list @t4)) % 123.27/123.51 (define @t23 () (not (forall @t22 (or @t21 @t12 @t7)))) % 123.27/123.51 (define @t24 () (@var "B" tptp.term)) % 123.27/123.51 (define @t25 () (_ @t14 tptp.id)) % 123.27/123.51 (define @t26 () (_ tptp.ap @t25)) % 123.27/123.51 (define @t27 () (not (_ (_ @t3 @t24) tptp.id))) % 123.27/123.51 (define @t28 () (@list @t8 @t24)) % 123.27/123.51 (define @t29 () (not (forall @t28 (or @t10 @t27 (_ (_ @t3 (_ @t26 @t24)) tptp.id))))) % 123.27/123.51 (define @t30 () (@var "K" tptp.subst)) % 123.27/123.51 (define @t31 () (_ (_ (_ @t2 @t16) @t8) (_ (_ tptp.comp @t30) @t13))) % 123.27/123.51 (define @t32 () (_ (_ (_ @t2 (_ @t17 @t30)) (_ @t14 @t30)) @t13)) % 123.27/123.51 (define @t33 () (@list @t16 @t8 @t13 @t30)) % 123.27/123.51 (define @t34 () (not (forall @t33 (or (not @t32) @t31)))) % 123.27/123.51 (define @t35 () (not (forall @t33 (or (not @t31) @t32)))) % 123.27/123.51 (define @t36 () (forall (@list @t2 @t1) (or @t35 @t34 (not (forall @t11 (or (not (_ tptp.var @t25)) @t9))) @t29 @t23 (_ (_ @t3 @t1) tptp.id)))) % 123.27/123.51 (define @t37 () (@var "Bound_variable_2931" tptp.term)) % 123.27/123.51 (define @t38 () (@var "Q" (-> tptp.term Bool))) % 123.27/123.51 (define @t39 () (_ tptp.push @t24)) % 123.27/123.51 (define @t40 () (_ @t39 tptp.id)) % 123.27/123.51 (define @t41 () (not (_ @t38 @t24))) % 123.27/123.51 (define @t42 () (@list @t24)) % 123.27/123.51 (define @t43 () (@var "X" tptp.term)) % 123.27/123.51 (define @t44 () (_ @t38 @t43)) % 123.27/123.51 (define @t45 () (@list @t43)) % 123.27/123.51 (define @t46 () (forall @t45 (= @t44 (_ (_ @t3 @t43) tptp.id)))) % 123.27/123.51 (define @t47 () (not @t46)) % 123.27/123.51 (define @t48 () (forall (@list @t2 @t38 @t37) (or @t23 @t47 (not (forall @t42 (or @t41 (_ @t38 (_ (_ tptp.sub @t37) @t40))))) (_ @t38 (_ tptp.lam @t37))))) % 123.27/123.51 (define @t49 () (forall @t11 (= @t8 @t25))) % 123.27/123.51 (define @t50 () (@var "Bound_variable_2367" tptp.term)) % 123.27/123.51 (define @t51 () (@var "P" (-> tptp.term Bool))) % 123.27/123.51 (define @t52 () (_ tptp.lam @t8)) % 123.27/123.51 (define @t53 () (_ @t51 @t52)) % 123.27/123.51 (define @t54 () (not (_ @t51 @t24))) % 123.27/123.51 (define @t55 () (not (forall @t11 (or (not (forall @t42 (or @t54 (_ @t51 (_ @t14 @t40))))) @t53)))) % 123.27/123.51 (define @t56 () (_ tptp.ap @t8)) % 123.27/123.51 (define @t57 () (_ @t51 @t8)) % 123.27/123.51 (define @t58 () (not @t57)) % 123.27/123.51 (define @t59 () (not (forall @t28 (or @t58 @t54 (_ @t51 (_ @t56 @t24)))))) % 123.27/123.51 (define @t60 () (not (forall @t11 (or (not (_ tptp.var @t8)) @t57)))) % 123.27/123.51 (define @t61 () (forall (@list @t51 @t50) (or @t60 @t59 @t55 (_ @t51 @t50)))) % 123.27/123.51 (define @t62 () (@list @t38)) % 123.27/123.51 (define @t63 () (forall (@list @t2) (not (forall @t62 @t47)))) % 123.27/123.51 (define @t64 () (@var "Bound_variable_2910" tptp.term)) % 123.27/123.51 (define @t65 () (forall (@list @t2 @t38 @t64) (or @t35 @t34 @t23 @t47 (not (forall @t42 (or @t41 (_ @t38 (_ (_ tptp.sub @t64) @t40))))) (_ @t38 (_ tptp.lam @t64))))) % 123.27/123.51 (define @t66 () (_ (_ tptp.push @t8) @t16)) % 123.27/123.51 (define @t67 () (_ tptp.sub @t43)) % 123.27/123.51 (define @t68 () (_ @t67 @t66)) % 123.27/123.51 (define @t69 () (_ @t51 @t68)) % 123.27/123.51 (define @t70 () (= @t44 @t69)) % 123.27/123.51 (define @t71 () (forall @t45 @t70)) % 123.27/123.51 (define @t72 () (not @t71)) % 123.27/123.51 (define @t73 () (forall (@list @t51 @t8 @t16) (not (forall @t62 @t72)))) % 123.27/123.51 (define @t74 () (_ tptp.comp tptp.sh)) % 123.27/123.51 (define @t75 () (@list @t8 @t16)) % 123.27/123.51 (define @t76 () (forall @t75 (= @t16 (_ @t74 @t66)))) % 123.27/123.51 (define @t77 () (@var "K" (-> tptp.term Bool))) % 123.27/123.51 (define @t78 () (forall (@list @t51 @t77 @t8 @t16 @t24) (or @t58 (_ @t77 (_ @t14 (_ @t39 @t16)))))) % 123.27/123.51 (define @t79 () (_ tptp.sub tptp.one)) % 123.27/123.51 (define @t80 () (forall @t75 (= @t8 (_ @t79 @t66)))) % 123.27/123.51 (define @t81 () (@var "Bound_variable_2605" tptp.term)) % 123.27/123.51 (define @t82 () (@var "Bound_variable_2603" tptp.term)) % 123.27/123.51 (define @t83 () (_ tptp.d2subst tptp.d_id)) % 123.27/123.51 (define @t84 () (_ tptp.d2term tptp.d_one)) % 123.27/123.51 (define @t85 () (@var "Bound_variable_3295" tptp.term)) % 123.27/123.51 (define @t86 () (forall (@list @t2 @t85) (or @t29 @t23 (_ (_ @t3 @t85) tptp.id)))) % 123.27/123.51 (define @t87 () (@var "Bound_variable_3232" tptp.term)) % 123.27/123.51 (define @t88 () (forall (@list @t2 @t87) (or @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t87) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t87)) tptp.id)))) % 123.27/123.51 (define @t89 () (@list @t16)) % 123.27/123.51 (define @t90 () (forall @t89 (= @t16 (_ @t17 tptp.id)))) % 123.27/123.51 (define @t91 () (forall @t89 (= @t16 (_ (_ tptp.comp tptp.id) @t16)))) % 123.27/123.51 (define @t92 () (and @t91 @t90)) % 123.27/123.51 (define @t93 () (_ (_ tptp.push tptp.one) tptp.sh)) % 123.27/123.51 (define @t94 () (_ tptp.sub @t24)) % 123.27/123.51 (define @t95 () (forall @t42 (not (forall @t22 (not (= @t5 (_ @t94 @t93))))))) % 123.27/123.51 (define @t96 () (@var "Bound_variable_2342" tptp.subst)) % 123.27/123.51 (define @t97 () (@var "Bound_variable_2340" tptp.term)) % 123.27/123.51 (define @t98 () (_ tptp.var @t24)) % 123.27/123.51 (define @t99 () (not @t98)) % 123.27/123.51 (define @t100 () (forall (@list @t51 @t97 @t96) (or @t59 @t55 (not (forall @t42 (or @t99 (_ @t51 (_ @t94 @t96))))) (_ @t51 (_ (_ tptp.sub @t97) @t96))))) % 123.27/123.51 (define @t101 () (forall @t42 (not (forall @t22 (not (forall @t75 (= (_ @t94 @t66) @t19))))))) % 123.27/123.51 (define @t102 () (@var "Bound_variable_3211" tptp.term)) % 123.27/123.51 (define @t103 () (forall (@list @t2 @t102) (or @t35 @t34 @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ (_ tptp.sub @t102) @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam @t102)) tptp.id)))) % 123.27/123.51 (define @t104 () (@var "Bound_variable_3046" tptp.term)) % 123.27/123.51 (define @t105 () (_ tptp.sub @t104)) % 123.27/123.51 (define @t106 () (forall (@list @t2 @t104) (or @t23 (not (forall @t42 (or @t27 (_ (_ @t3 (_ @t105 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t105 @t93))) tptp.id)))) % 123.27/123.51 (define @t107 () (= @t8 @t24)) % 123.27/123.51 (define @t108 () (forall @t28 (or (not (= @t52 (_ tptp.lam @t24))) @t107))) % 123.27/123.51 (define @t109 () (@var "Bound_variable_2551" tptp.term)) % 123.27/123.51 (define @t110 () (@var "Bound_variable_2549" tptp.subst)) % 123.27/123.51 (define @t111 () (@var "Bound_variable_2547" (-> tptp.subst tptp.term tptp.term))) % 123.27/123.51 (define @t112 () (forall (@list @t4 @t111 @t110 @t109) (or @t21 (not (forall @t20 (= (_ (_ tptp.sub (_ (_ @t111 @t16) @t8)) @t13) (_ (_ @t111 @t18) @t15)))) (not (= @t6 (_ tptp.lam (_ (_ @t111 tptp.sh) tptp.one)))) (= (_ (_ @t4 @t110) @t109) (_ (_ @t111 @t110) @t109))))) % 123.27/123.51 (define @t113 () (@var "D" tptp.term)) % 123.27/123.51 (define @t114 () (@var "C" tptp.term)) % 123.27/123.51 (define @t115 () (not (= (_ @t26 @t114) (_ (_ tptp.ap (_ @t94 tptp.id)) @t113)))) % 123.27/123.51 (define @t116 () (@list @t8 @t24 @t114 @t113)) % 123.27/123.51 (define @t117 () (forall @t116 (or @t115 @t107))) % 123.27/123.51 (define @t118 () (not (= (_ @t56 @t114) (_ (_ tptp.ap @t24) @t113)))) % 123.27/123.51 (define @t119 () (forall @t116 (or @t118 @t107))) % 123.27/123.51 (define @t120 () (= @t114 @t113)) % 123.27/123.51 (define @t121 () (forall @t116 (or @t115 @t120))) % 123.27/123.51 (define @t122 () (forall @t116 (or @t118 @t120))) % 123.27/123.51 (define @t123 () (@var "Bound_variable_2822" tptp.term)) % 123.27/123.51 (define @t124 () (@var "Bound_variable_2820" tptp.term)) % 123.27/123.51 (define @t125 () (@var "Bound_variable_2140" tptp.term)) % 123.27/123.51 (define @t126 () (forall (@list @t51 @t125) (or @t60 @t59 (not (forall @t11 (or @t58 @t53))) (_ @t51 @t125)))) % 123.27/123.51 (define @t127 () (@list @t51 @t38 @t8 @t16)) % 123.27/123.51 (define @t128 () (forall @t127 (or @t58 @t72 (_ @t38 tptp.one)))) % 123.27/123.51 (define @t129 () (@var "Bound_variable_3001" tptp.term)) % 123.27/123.51 (define @t130 () (@var "Bound_variable_2999" tptp.term)) % 123.27/123.51 (define @t131 () (forall (@list @t2 @t130 @t129) (or @t35 @t34 @t29 (not (_ (_ @t3 @t130) tptp.id)) (not (_ (_ @t3 @t129) tptp.id)) (_ (_ @t3 (_ (_ tptp.ap @t130) @t129)) tptp.id)))) % 123.27/123.51 (define @t132 () (@var "Bound_variable_3171" tptp.term)) % 123.27/123.51 (define @t133 () (_ tptp.sub @t132)) % 123.27/123.51 (define @t134 () (@var "Bound_variable_3094" tptp.subst)) % 123.27/123.51 (define @t135 () (@var "Bound_variable_3090" tptp.subst)) % 123.27/123.51 (define @t136 () (_ (_ tptp.comp @t135) @t134)) % 123.27/123.51 (define @t137 () (@var "Bound_variable_3092" tptp.term)) % 123.27/123.51 (define @t138 () (_ (_ tptp.sub @t137) @t134)) % 123.27/123.51 (define @t139 () (@var "Bound_variable_3149" tptp.term)) % 123.27/123.51 (define @t140 () (_ tptp.sub @t139)) % 123.27/123.51 (define @t141 () (@var "Bound_variable_3076" tptp.subst)) % 123.27/123.51 (define @t142 () (@var "Bound_variable_3072" tptp.subst)) % 123.27/123.51 (define @t143 () (@var "Bound_variable_3074" tptp.term)) % 123.27/123.51 (define @t144 () (_ tptp.var @t84)) % 123.27/123.51 (define @t145 () (not @t144)) % 123.27/123.51 (define @t146 () (@list @t8 @t16 @t51 @t38)) % 123.27/123.51 (define @t147 () (lambda @t146 @t71)) % 123.27/123.51 (define @t148 () (= tptp.pushprop_p_and_p_prime @t147)) % 123.27/123.51 (define @t149 () (@var "DS2" tptp.d_subst)) % 123.27/123.51 (define @t150 () (@var "DS1" tptp.d_subst)) % 123.27/123.51 (define @t151 () (@var "DS" tptp.d_subst)) % 123.27/123.51 (define @t152 () (@list @t151)) % 123.27/123.51 (define @t153 () (@var "S" tptp.subst)) % 123.27/123.51 (define @t154 () (@var "DT2" tptp.d_term)) % 123.27/123.51 (define @t155 () (@var "DT1" tptp.d_term)) % 123.27/123.51 (define @t156 () (@var "DT" tptp.d_term)) % 123.27/123.51 (define @t157 () (@list @t156)) % 123.27/123.51 (define @t158 () (forall @t157 (= @t156 tptp.d_one))) % 123.27/123.51 (define @t159 () (_ tptp.d2term @t156)) % 123.27/123.51 (define @t160 () (@var "T" tptp.term)) % 123.27/123.51 (define @t161 () (= @t160 @t159)) % 123.27/123.51 (define @t162 () (exists @t157 @t161)) % 123.27/123.51 (define @t163 () (@list @t160)) % 123.27/123.51 (define @t164 () (forall @t163 @t162)) % 123.27/123.51 (define @t165 () (_ (_ tptp.sub @t114) tptp.sh)) % 123.27/123.51 (define @t166 () (_ @t38 @t165)) % 123.27/123.51 (define @t167 () (_ @t38 @t114)) % 123.27/123.51 (define @t168 () (=> @t167 @t166)) % 123.27/123.51 (define @t169 () (_ tptp.var @t114)) % 123.27/123.51 (define @t170 () (@list @t114)) % 123.27/123.51 (define @t171 () (forall @t170 (=> @t169 @t168))) % 123.27/123.51 (define @t172 () (_ @t94 @t16)) % 123.27/123.51 (define @t173 () (_ @t51 @t172)) % 123.27/123.51 (define @t174 () (forall @t42 (=> @t98 @t173))) % 123.27/123.51 (define @t175 () (=> @t174 @t171)) % 123.27/123.51 (define @t176 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t8) @t16) @t51) @t38)) % 123.27/123.51 (define @t177 () (=> @t176 @t175)) % 123.27/123.51 (define @t178 () (forall @t127 @t177)) % 123.27/123.51 (define @t179 () (= tptp.pushprop_lem2v2 @t178)) % 123.27/123.51 (define @t180 () (not @t179)) % 123.27/123.51 (define @t181 () (tptp.d2term tptp.d_one)) % 123.27/123.51 (define @t182 () (tptp.var @t181)) % 123.27/123.51 (define @t183 () (tptp.d2subst tptp.d_id)) % 123.27/123.51 (define @t184 () (@var "BOUND_VARIABLE_9058" tptp.term)) % 123.27/123.51 (define @t185 () (not (_ @t38 @t184))) % 123.27/123.51 (define @t186 () (not (tptp.var @t184))) % 123.27/123.51 (define @t187 () (tptp.sub @t24 @t16)) % 123.27/123.51 (define @t188 () (_ @t51 @t187)) % 123.27/123.51 (define @t189 () (tptp.var @t24)) % 123.27/123.51 (define @t190 () (not @t189)) % 123.27/123.51 (define @t191 () (forall @t42 (or @t190 @t188))) % 123.27/123.51 (define @t192 () (not @t191)) % 123.27/123.51 (define @t193 () (tptp.push @t8 @t16)) % 123.27/123.51 (define @t194 () (tptp.sub @t43 @t193)) % 123.27/123.51 (define @t195 () (_ @t51 @t194)) % 123.27/123.51 (define @t196 () (_ @t38 @t43)) % 123.27/123.51 (define @t197 () (forall @t45 (= @t196 @t195))) % 123.27/123.51 (define @t198 () (not @t197)) % 123.27/123.51 (define @t199 () (@list @t51 @t38 @t8 @t16 @t184)) % 123.27/123.51 (define @t200 () (forall @t199 (or @t198 @t192 @t186 @t185 (_ @t38 (tptp.sub @t184 @t183))))) % 123.27/123.51 (define @t201 () (@quantifiers_skolemize @t200 4)) % 123.27/123.51 (define @t202 () (tptp.d2term @t156)) % 123.27/123.51 (define @t203 () (forall @t157 (not (= @t202 @t201)))) % 123.27/123.51 (define @t204 () (@quantifiers_skolemize @t203 0)) % 123.27/123.51 (define @t205 () (tptp.d2term @t204)) % 123.27/123.51 (define @t206 () (not @t161)) % 123.27/123.51 (define @t207 () (forall @t157 @t206)) % 123.27/123.51 (define @t208 () (not @t207)) % 123.27/123.51 (define @t209 () (not (= @t201 @t202))) % 123.27/123.51 (define @t210 () (forall @t157 @t209)) % 123.27/123.51 (define @t211 () (not @t210)) % 123.27/123.51 (define @t212 () (forall @t163 (not (forall @t157 (not (= @t160 @t202)))))) % 123.27/123.51 (define @t213 () (not @t203)) % 123.27/123.51 (define @t214 () (= @t201 @t205)) % 123.27/123.51 (define @t215 () (= @t205 @t201)) % 123.27/123.51 (define @t216 () (not (not @t215))) % 123.27/123.51 (define @t217 () (@list true)) % 123.27/123.51 (define @t218 () (tptp.var @t201)) % 123.27/123.51 (define @t219 () (tptp.sub @t184 @t83)) % 123.27/123.51 (define @t220 () (_ @t38 @t219)) % 123.27/123.51 (define @t221 () (or @t198 @t192 @t186 @t185 @t220)) % 123.27/123.51 (define @t222 () (_ (lambda @t146 @t197) @t8 @t16 @t51 @t38)) % 123.27/123.51 (define @t223 () (not @t222)) % 123.27/123.51 (define @t224 () (or @t223 @t192 @t186 @t185 @t220)) % 123.27/123.51 (define @t225 () (forall @t199 @t224)) % 123.27/123.51 (define @t226 () (tptp.sub @t184 tptp.sh)) % 123.27/123.51 (define @t227 () (_ @t38 @t226)) % 123.27/123.51 (define @t228 () (tptp.pushprop_p_and_p_prime @t8 @t16 @t51 @t38)) % 123.27/123.51 (define @t229 () (not @t228)) % 123.27/123.51 (define @t230 () (or @t229 @t192 @t186 @t185 @t227)) % 123.27/123.51 (define @t231 () (forall @t199 @t230)) % 123.27/123.51 (define @t232 () (= tptp.pushprop_lem2v2 @t231)) % 123.27/123.51 (define @t233 () (or @t186 @t185 @t227)) % 123.27/123.51 (define @t234 () (or @t229 @t192 @t233)) % 123.27/123.51 (define @t235 () (forall @t199 @t234)) % 123.27/123.51 (define @t236 () (@list @t184)) % 123.27/123.51 (define @t237 () (forall @t236 @t234)) % 123.27/123.51 (define @t238 () (forall @t236 @t233)) % 123.27/123.51 (define @t239 () (or @t229 @t192 @t238)) % 123.27/123.51 (define @t240 () (tptp.sub @t114 tptp.sh)) % 123.27/123.51 (define @t241 () (_ @t38 @t240)) % 123.27/123.51 (define @t242 () (_ @t38 @t114)) % 123.27/123.51 (define @t243 () (tptp.var @t114)) % 123.27/123.51 (define @t244 () (forall @t170 (or (not @t243) (not @t242) @t241))) % 123.27/123.51 (define @t245 () (not @t176)) % 123.27/123.51 (define @t246 () (or @t245 @t192 @t244)) % 123.27/123.51 (define @t247 () (=> @t191 @t244)) % 123.27/123.51 (define @t248 () (not @t167)) % 123.27/123.51 (define @t249 () (not @t169)) % 123.27/123.51 (define @t250 () (or @t249 @t248 @t166)) % 123.27/123.51 (define @t251 () (or @t99 @t173)) % 123.27/123.51 (define @t252 () (@quantifiers_skolemize @t200 1)) % 123.27/123.51 (define @t253 () (not @t218)) % 123.27/123.51 (define @t254 () (@quantifiers_skolemize @t200 3)) % 123.27/123.51 (define @t255 () (@quantifiers_skolemize @t200 0)) % 123.27/123.51 (define @t256 () (or (not (forall @t45 (= (_ @t252 @t43) (_ @t255 (tptp.sub @t43 (tptp.push (@quantifiers_skolemize @t200 2) @t254)))))) (not (forall @t42 (or @t190 (_ @t255 (tptp.sub @t24 @t254))))) @t253 (not (_ @t252 @t201)) (_ @t252 (tptp.sub @t201 @t183)))) % 123.27/123.51 (assume @p1 (and @t164 @t158 (forall (@list @t155 @t154) (=> (= (_ tptp.d2term @t155) (_ tptp.d2term @t154)) (= @t155 @t154))) (forall (@list @t153) (exists @t152 (= @t153 (_ tptp.d2subst @t151)))) (forall @t152 (= @t151 tptp.d_id)) (forall (@list @t150 @t149) (=> (= (_ tptp.d2subst @t150) (_ tptp.d2subst @t149)) (= @t150 @t149))) (= tptp.one @t84) (= (_ (_ tptp.ap @t84) @t84) @t84) (= (_ tptp.lam @t84) @t84) (= (_ (_ tptp.sub @t84) @t83) @t84) (= tptp.id @t83) (= tptp.sh @t83) (= (_ (_ tptp.push @t84) @t83) @t83) (= (_ (_ tptp.comp @t83) @t83) @t83) (= (_ (_ (_ (_ tptp.hoasap @t83) @t84) @t83) @t84) @t84) (= tptp.hoaslam (lambda (@list (@var "Bound_variable_4913" tptp.subst) (@var "Bound_variable_4915" (-> tptp.subst tptp.term tptp.term))) @t84)) (= tptp.hoasinduction_p_and_p_prime (lambda (@list @t2 @t38) @t46)) @t148 @t145 (= tptp.pushprop_lem1v2 @t128) tptp.pushprop_lem1_gthm tptp.axmap tptp.pushprop_lem0_gthm (= tptp.shinj (forall @t28 (or (not (= (_ @t14 tptp.sh) (_ @t94 tptp.sh))) @t107))) tptp.hoasinduction_lem1v2 tptp.hoasinduction_lem1v2_gthm (= tptp.induction2lem @t100) (= tptp.hoasinduction_lem3v2_f @t101) tptp.axvarshift (= tptp.hoasapinj2 @t121) tptp.hoasapnotvar_gthm (= tptp.hoasapinj1 @t117) (not tptp.ulamvar1) (= tptp.induction2lem_lthm (=> @t80 (=> @t76 (=> @t90 (=> @t126 @t100))))) tptp.hoasinduction_lem3v2_gthm tptp.apnotvar tptp.pushprop_lthm_orig (= tptp.hoasinduction_lem3v2_f_lthm @t101) (= tptp.hoasinduction_lthm (=> @t61 (=> @t131 (=> @t103 @t36)))) (= tptp.hoasinduction_no_psi_cond_lthm (=> @t63 (=> @t61 (=> @t49 (=> @t48 @t86))))) (= tptp.hoaslaminj @t112) (= tptp.hoasinduction_lem3aaa (forall (@list @t2 @t132) (or (not (forall (@list @t4 @t139) (or @t12 @t7 (not (forall (@list @t142 @t143 @t141) (= (_ (_ tptp.sub (_ (_ @t4 @t142) @t143)) @t141) (_ (_ tptp.sub (_ @t140 (_ (_ tptp.push @t143) @t142))) @t141)))) (not (forall (@list @t135 @t137 @t134) (= (_ (_ @t4 @t136) @t138) (_ @t140 (_ (_ tptp.push @t138) @t136)))))))) (not (forall @t42 (or @t27 (_ (_ @t3 (_ @t133 @t40)) tptp.id)))) (_ (_ @t3 (_ tptp.lam (_ @t133 @t93))) tptp.id)))) tptp.induction2lem_gthm (= tptp.hoasinduction_lem3aa_lthm @t106) (= tptp.hoasinduction_lem3 @t103) (= tptp.hoasinduction_lem2 @t131) (= tptp.termmset_lthm (=> @t49 @t49)) tptp.hoasinduction_lem1 tptp.hoaslamnotap_lthm (= tptp.pushprop_lem1v2_lthm (=> @t80 @t128)) tptp.hoasapnotvar (= tptp.hoasinduction_lem0 @t63) (= tptp.hoasinduction @t36) tptp.hoasinduction_gthm tptp.axapp tptp.hoaslamnotvar_lthm tptp.pushprop_lem3v2_lthm (= tptp.hoasinduction_lem3b_lthm @t95) tptp.ulamvarind (= tptp.induction @t126) (= tptp.hoasinduction_lem3a_lthm (=> @t49 (=> @t106 @t88))) tptp.termmset_gthm (= tptp.hoasinduction_lem3aa @t106) tptp.pushprop_lem1v2_gthm tptp.hoaslamnotap_gthm tptp.hoaslamnotvar_gthm tptp.hoasinduction_lem3b_gthm tptp.pushprop_lem2v2 tptp.hoasinduction_lem3a_gthm tptp.axclos tptp.axassoc (= tptp.hoasinduction_lem2v2 (forall (@list @t2 @t38 @t124 @t123) (or @t35 @t34 @t29 @t47 (not (_ @t38 @t124)) (not (_ @t38 @t123)) (_ @t38 (_ (_ tptp.ap @t124) @t123))))) tptp.pushprop_lthm (= tptp.apinj2 @t122) (= tptp.apinj1 @t119) (= tptp.hoasapinj2_lthm (=> @t122 @t121)) (= tptp.hoasinduction_lem3v2a @t48) (= tptp.hoasapinj1_lthm (=> @t49 (=> @t119 @t117))) (= tptp.hoaslaminj_lthm (=> @t80 (=> @t76 (=> @t108 @t112)))) (= 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 @t108) (= tptp.hoasinduction_lem3_lthm (=> @t49 (=> @t106 @t103))) (= tptp.pushprop_lem0 @t73) tptp.pushprop_gthm tptp.axabs (= tptp.hoasinduction_lem3v2a_lthm (=> @t101 (=> @t49 @t48))) 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 (=> @t49 (=> @t100 @t61))) (= tptp.hoasinduction_lem0_lthm @t63) (= 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 @t21 (not (= @t6 (_ (_ tptp.ap (_ (_ tptp.sub @t82) tptp.id)) @t81)))))) tptp.substmonoid_gthm tptp.ulamvarsh (= tptp.induction2 @t61) tptp.pushprop_lem3v2 tptp.pushprop_lem2v2_gthm (= tptp.pushprop_lem1_lthm (=> @t80 (=> @t76 @t78))) (= tptp.hoasinduction_lem3v2 @t65) (= tptp.axshiftcons @t76) (= tptp.termmset @t49) (= tptp.pushprop_lem0_lthm @t73) tptp.hoasapnotvar_lthm (= tptp.hoasinduction_lem3v2_lthm (=> @t49 @t65)) (= tptp.axvarid @t49) (= tptp.hoasinduction_lthm_3 (=> @t63 (=> @t61 (=> @t49 (=> @t48 @t36))))))) % 123.27/123.51 (assume @p2 @t180) % 123.27/123.51 (assume @p3 true) % 123.27/123.51 (step @p4 :rule evaluate :args ((= true false))) % 123.27/123.51 (step @p5 :rule refl :args ((tptp.var @t84))) % 123.27/123.51 (step @p6 :rule refl :args (@t181)) % 123.27/123.51 (step @p7 :rule cong :premises (@p6) :args (@t182)) % 123.27/123.51 (step @p8 :rule trans :premises (@p7 @p5)) % 123.27/123.51 (step @p9 :rule refl :args (tptp.var)) % 123.27/123.51 (step @p10 :rule ho_cong :premises (@p9 @p6)) % 123.27/123.51 (step @p11 :rule cong :premises (@p10 @p8) :args ((= (_ tptp.var @t181) @t182))) % 123.27/123.51 (step @p12 :rule symm :premises (@p11)) % 123.27/123.51 (step @p13 :rule refl :args (@t144)) % 123.27/123.51 (step @p14 :rule eq_resolve :premises (@p13 @p12)) % 123.27/123.51 (step @p15 :rule refl :args (@t84)) % 123.27/123.51 (step @p16 :rule cong :premises (@p15 @p6) :args ((= @t84 @t181))) % 123.27/123.51 (step @p17 :rule symm :premises (@p16)) % 123.27/123.51 (step @p18 :rule eq_resolve :premises (@p15 @p17)) % 123.27/123.51 (step @p19 :rule refl :args (tptp.var)) % 123.27/123.51 (step @p20 :rule ho_cong :premises (@p19 @p18)) % 123.27/123.51 (step @p21 :rule trans :premises (@p20 @p14)) % 123.27/123.51 (step @p22 :rule cong :premises (@p21) :args (@t145)) % 123.27/123.51 (step @p23 :rule and_elim :premises (@p1) :args (18)) % 123.27/123.51 (step @p24 :rule eq_resolve :premises (@p23 @p22)) % 123.27/123.51 (step @p25 :rule false_intro :premises (@p24)) % 123.27/123.51 (step @p26 :rule eq-symm :args (@t156 tptp.d_one)) % 123.27/123.51 (step @p27 :rule cong :premises (@p26) :args (@t158)) % 123.27/123.51 (step @p28 :rule and_elim :premises (@p1) :args (1)) % 123.27/123.51 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 123.27/123.51 (step @p30 :rule instantiate :premises (@p29) :args ((@list @t204))) % 123.27/123.51 (step @p31 :rule symm :premises (@p30)) % 123.27/123.51 (step @p32 :rule cong :premises (@p31) :args (@t205)) % 123.27/123.51 (step @p33 :rule refl :args (@t202)) % 123.27/123.51 (step @p34 :rule refl :args (@t159)) % 123.27/123.51 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t159 @t202))) % 123.27/123.51 (step @p36 :rule symm :premises (@p35)) % 123.27/123.51 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 123.27/123.51 (step @p38 :rule refl :args (@t160)) % 123.27/123.51 (step @p39 :rule cong :premises (@p38 @p37) :args (@t161)) % 123.27/123.51 (step @p40 :rule cong :premises (@p39) :args (@t206)) % 123.27/123.51 (step @p41 :rule cong :premises (@p40) :args (@t207)) % 123.27/123.51 (step @p42 :rule cong :premises (@p41) :args (@t208)) % 123.27/123.51 (step @p43 :rule exists-elim :args ((= @t162 @t208))) % 123.27/123.51 (step @p44 :rule trans :premises (@p43 @p42)) % 123.27/123.51 (step @p45 :rule cong :premises (@p44) :args (@t164)) % 123.27/123.51 (step @p46 :rule and_elim :premises (@p1) :args (0)) % 123.27/123.51 (step @p47 :rule eq_resolve :premises (@p46 @p45)) % 123.27/123.51 (step @p48 :rule eq-symm :args (@t201 @t202)) % 123.27/123.51 (step @p49 :rule cong :premises (@p48) :args (@t209)) % 123.27/123.51 (step @p50 :rule cong :premises (@p49) :args (@t210)) % 123.27/123.51 (step @p51 :rule cong :premises (@p50) :args (@t211)) % 123.27/123.51 (step @p52 :rule refl :args (@t212)) % 123.27/123.51 (step @p53 :rule cong :premises (@p52 @p51) :args ((=> @t212 @t211))) % 123.27/123.51 (assume-push @p284 @t212) % 123.27/123.51 (step @p55 :rule instantiate :premises (@p47) :args ((@list @t201))) % 123.27/123.51 (step-pop @p285 :rule scope :premises (@p55)) % 123.27/123.51 (step @p56 :rule process_scope :premises (@p285) :args (@t211)) % 123.27/123.51 (step @p58 :rule eq_resolve :premises (@p56 @p53)) % 123.27/123.51 (step @p59 :rule implies_elim :premises (@p58)) % 123.27/123.51 (step @p60 :rule chain_m_resolution :premises (@p59 @p47) :args (@t213 (@list false) (@list @t212))) % 123.27/123.51 (step @p61 :rule refl :args (@t214)) % 123.27/123.51 (step @p62 :rule bool-double-not-elim :args (@t203)) % 123.27/123.51 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or (not @t213) @t214))) % 123.27/123.51 (step @p64 :rule eq-symm :args (@t205 @t201)) % 123.27/123.51 (step @p65 :rule bool-double-not-elim :args (@t215)) % 123.27/123.51 (step @p66 :rule trans :premises (@p65 @p64)) % 123.27/123.51 (step @p67 :rule refl :args (@t213)) % 123.27/123.51 (step @p68 :rule cong :premises (@p67 @p66) :args ((=> @t213 @t216))) % 123.27/123.51 (assume-push @p286 @t213) % 123.27/123.51 (step @p70 :rule skolemize :premises (@p60)) % 123.27/123.51 (step-pop @p287 :rule scope :premises (@p70)) % 123.27/123.51 (step @p71 :rule process_scope :premises (@p287) :args (@t216)) % 123.27/123.51 (step @p73 :rule eq_resolve :premises (@p71 @p68)) % 123.27/123.51 (step @p74 :rule implies_elim :premises (@p73)) % 123.27/123.51 (step @p75 :rule eq_resolve :premises (@p74 @p63)) % 123.27/123.51 (step @p76 :rule chain_m_resolution :premises (@p75 @p60) :args (@t214 @t217 (@list @t203))) % 123.27/123.51 (step @p77 :rule trans :premises (@p76 @p32)) % 123.27/123.51 (step @p78 :rule cong :premises (@p77) :args (@t218)) % 123.27/123.51 (step @p79 :rule refl :args (@t183)) % 123.27/123.51 (step @p80 :rule refl :args (@t83)) % 123.27/123.51 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t83 @t183))) % 123.27/123.51 (step @p82 :rule symm :premises (@p81)) % 123.27/123.51 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 123.27/123.51 (step @p84 :rule refl :args (@t184)) % 123.27/123.51 (step @p85 :rule cong :premises (@p84 @p83) :args (@t219)) % 123.27/123.51 (step @p86 :rule cong :premises (@p85) :args (@t220)) % 123.27/123.51 (step @p87 :rule refl :args (@t185)) % 123.27/123.51 (step @p88 :rule refl :args (@t186)) % 123.27/123.51 (step @p89 :rule refl :args (@t192)) % 123.27/123.51 (step @p90 :rule refl :args (@t198)) % 123.27/123.51 (step @p91 :rule nary_cong :premises (@p90 @p89 @p88 @p87 @p86) :args (@t221)) % 123.27/123.51 (step @p92 :rule cong :premises (@p91) :args ((forall @t199 @t221))) % 123.27/123.51 (step @p93 :rule refl :args (@t220)) % 123.27/123.51 (step @p94 :rule refl :args (@t185)) % 123.27/123.51 (step @p95 :rule refl :args (@t186)) % 123.27/123.51 (step @p96 :rule refl :args (@t192)) % 123.27/123.51 (step @p97 :rule beta-reduce :args ((= @t222 @t197))) % 123.27/123.51 (step @p98 :rule cong :premises (@p97) :args (@t223)) % 123.27/123.51 (step @p99 :rule nary_cong :premises (@p98 @p96 @p95 @p94 @p93) :args (@t224)) % 123.27/123.51 (step @p100 :rule cong :premises (@p99) :args (@t225)) % 123.27/123.51 (step @p101 :rule trans :premises (@p100 @p92)) % 123.27/123.51 (step @p102 :rule bool-eq-true :args (@t225)) % 123.27/123.51 (step @p103 :rule eq-symm :args (true @t225)) % 123.27/123.51 (step @p104 :rule trans :premises (@p103 @p102)) % 123.27/123.51 (step @p105 :rule trans :premises (@p104 @p101)) % 123.27/123.51 (step @p106 :rule cong :premises (@p105) :args ((not (= true @t225)))) % 123.27/123.51 (step @p107 :rule and_elim :premises (@p1) :args (11)) % 123.27/123.51 (step @p108 :rule refl :args (@t184)) % 123.27/123.51 (step @p109 :rule cong :premises (@p108 @p107) :args (@t226)) % 123.27/123.51 (step @p110 :rule cong :premises (@p109) :args (@t227)) % 123.27/123.51 (step @p111 :rule refl :args (@t38)) % 123.27/123.51 (step @p112 :rule refl :args (@t51)) % 123.27/123.51 (step @p113 :rule refl :args (@t16)) % 123.27/123.51 (step @p114 :rule refl :args (@t8)) % 123.27/123.51 (step @p115 :rule refl :args ((_ @t51 @t68))) % 123.27/123.51 (step @p116 :rule refl :args ((tptp.sub @t43 @t66))) % 123.27/123.51 (step @p117 :rule refl :args (@t193)) % 123.27/123.51 (step @p118 :rule refl :args (@t43)) % 123.27/123.51 (step @p119 :rule cong :premises (@p118 @p117) :args (@t194)) % 123.27/123.51 (step @p120 :rule trans :premises (@p119 @p116)) % 123.27/123.51 (step @p121 :rule cong :premises (@p120) :args (@t195)) % 123.27/123.51 (step @p122 :rule trans :premises (@p121 @p115)) % 123.27/123.51 (step @p123 :rule refl :args (@t51)) % 123.27/123.51 (step @p124 :rule ho_cong :premises (@p123 @p120)) % 123.27/123.51 (step @p125 :rule cong :premises (@p124 @p122) :args ((= (_ @t51 @t194) @t195))) % 123.27/123.51 (step @p126 :rule symm :premises (@p125)) % 123.27/123.51 (step @p127 :rule refl :args (@t69)) % 123.27/123.51 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 123.27/123.51 (step @p129 :rule refl :args (@t67)) % 123.27/123.51 (step @p130 :rule ho_cong :premises (@p129 @p117)) % 123.27/123.51 (step @p131 :rule cong :premises (@p130 @p120) :args ((= (_ @t67 @t193) @t194))) % 123.27/123.51 (step @p132 :rule symm :premises (@p131)) % 123.27/123.51 (step @p133 :rule refl :args (@t68)) % 123.27/123.51 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 123.27/123.51 (step @p135 :rule refl :args (@t66)) % 123.27/123.51 (step @p136 :rule cong :premises (@p135 @p117) :args ((= @t66 @t193))) % 123.27/123.51 (step @p137 :rule symm :premises (@p136)) % 123.27/123.51 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 123.27/123.51 (step @p139 :rule ho_cong :premises (@p129 @p138)) % 123.27/123.51 (step @p140 :rule trans :premises (@p139 @p134)) % 123.27/123.51 (step @p141 :rule ho_cong :premises (@p123 @p140)) % 123.27/123.51 (step @p142 :rule trans :premises (@p141 @p128)) % 123.27/123.51 (step @p143 :rule refl :args (@t196)) % 123.27/123.51 (step @p144 :rule refl :args (@t44)) % 123.27/123.51 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t44 @t196))) % 123.27/123.51 (step @p146 :rule symm :premises (@p145)) % 123.27/123.51 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 123.27/123.51 (step @p148 :rule cong :premises (@p147 @p142) :args (@t70)) % 123.27/123.51 (step @p149 :rule cong :premises (@p148) :args (@t71)) % 123.27/123.51 (step @p150 :rule cong :premises (@p149) :args (@t147)) % 123.27/123.51 (step @p151 :rule refl :args (tptp.pushprop_p_and_p_prime)) % 123.27/123.51 (step @p152 :rule cong :premises (@p151 @p150) :args (@t148)) % 123.27/123.51 (step @p153 :rule and_elim :premises (@p1) :args (17)) % 123.27/123.51 (step @p154 :rule eq_resolve :premises (@p153 @p152)) % 123.27/123.51 (step @p155 :rule ho_cong :premises (@p154 @p114 @p113 @p112 @p111)) % 123.27/123.51 (step @p156 :rule cong :premises (@p155) :args (@t229)) % 123.27/123.51 (step @p157 :rule nary_cong :premises (@p156 @p96 @p95 @p94 @p110) :args (@t230)) % 123.27/123.51 (step @p158 :rule cong :premises (@p157) :args (@t231)) % 123.27/123.51 (step @p159 :rule bool-eq-true :args (tptp.pushprop_lem2v2)) % 123.27/123.51 (step @p160 :rule symm :premises (@p159)) % 123.27/123.51 (step @p161 :rule and_elim :premises (@p1) :args (67)) % 123.27/123.51 (step @p162 :rule eq_resolve :premises (@p161 @p160)) % 123.27/123.51 (step @p163 :rule cong :premises (@p162 @p158) :args (@t232)) % 123.27/123.51 (step @p164 :rule cong :premises (@p163) :args ((not @t232))) % 123.27/123.51 (step @p165 :rule trans :premises (@p164 @p106)) % 123.27/123.51 (step @p166 :rule aci_norm :args ((= @t234 @t230))) % 123.27/123.51 (step @p167 :rule cong :premises (@p166) :args (@t235)) % 123.27/123.51 (step @p168 :rule quant-merge-prenex :args ((= (forall @t127 @t237) @t235))) % 123.27/123.51 (step @p169 :rule alpha_equiv :args (@t238 (@list @t184) (@list @t114))) % 123.27/123.51 (step @p170 :rule refl :args (@t229)) % 123.27/123.51 (step @p171 :rule nary_cong :premises (@p170 @p89 @p169) :args (@t239)) % 123.27/123.51 (step @p172 :rule quant-miniscope-or :args ((= @t237 @t239))) % 123.27/123.51 (step @p173 :rule trans :premises (@p172 @p171)) % 123.27/123.51 (step @p174 :rule symm :premises (@p173)) % 123.27/123.51 (step @p175 :rule cong :premises (@p174) :args ((forall @t127 (or @t229 @t192 @t244)))) % 123.27/123.51 (step @p176 :rule trans :premises (@p175 @p168)) % 123.27/123.51 (step @p177 :rule trans :premises (@p176 @p167)) % 123.27/123.51 (step @p178 :rule refl :args (@t244)) % 123.27/123.51 (step @p179 :rule refl :args (@t228)) % 123.27/123.51 (step @p180 :rule refl :args (@t176)) % 123.27/123.51 (step @p181 :rule cong :premises (@p180 @p179) :args ((= @t176 @t228))) % 123.27/123.51 (step @p182 :rule symm :premises (@p181)) % 123.27/123.51 (step @p183 :rule eq_resolve :premises (@p180 @p182)) % 123.27/123.51 (step @p184 :rule cong :premises (@p183) :args (@t245)) % 123.27/123.51 (step @p185 :rule nary_cong :premises (@p184 @p89 @p178) :args (@t246)) % 123.27/123.51 (step @p186 :rule cong :premises (@p185) :args ((forall @t127 @t246))) % 123.27/123.51 (step @p187 :rule trans :premises (@p186 @p177)) % 123.27/123.51 (step @p188 :rule aci_norm :args ((= (or @t245 (or @t192 @t244)) @t246))) % 123.27/123.51 (step @p189 :rule bool-impl-elim :args (@t191 @t244)) % 123.27/123.51 (step @p190 :rule refl :args (@t245)) % 123.27/123.51 (step @p191 :rule nary_cong :premises (@p190 @p189) :args ((or @t245 @t247))) % 123.27/123.51 (step @p192 :rule trans :premises (@p191 @p188)) % 123.27/123.51 (step @p193 :rule bool-impl-elim :args (@t176 @t247)) % 123.27/123.51 (step @p194 :rule trans :premises (@p193 @p192)) % 123.27/123.51 (step @p195 :rule cong :premises (@p194) :args ((forall @t127 (=> @t176 @t247)))) % 123.27/123.51 (step @p196 :rule trans :premises (@p195 @p187)) % 123.27/123.51 (step @p197 :rule refl :args ((_ @t38 @t165))) % 123.27/123.51 (step @p198 :rule refl :args (@t240)) % 123.27/123.51 (step @p199 :rule cong :premises (@p198) :args (@t241)) % 123.27/123.51 (step @p200 :rule trans :premises (@p199 @p197)) % 123.27/123.51 (step @p201 :rule refl :args (@t38)) % 123.27/123.51 (step @p202 :rule ho_cong :premises (@p201 @p198)) % 123.27/123.51 (step @p203 :rule cong :premises (@p202 @p200) :args ((= (_ @t38 @t240) @t241))) % 123.27/123.51 (step @p204 :rule symm :premises (@p203)) % 123.27/123.51 (step @p205 :rule refl :args (@t166)) % 123.27/123.51 (step @p206 :rule eq_resolve :premises (@p205 @p204)) % 123.27/123.51 (step @p207 :rule refl :args (@t165)) % 123.27/123.51 (step @p208 :rule cong :premises (@p207 @p198) :args ((= @t165 @t240))) % 123.27/123.51 (step @p209 :rule symm :premises (@p208)) % 123.27/123.51 (step @p210 :rule eq_resolve :premises (@p207 @p209)) % 123.27/123.51 (step @p211 :rule ho_cong :premises (@p201 @p210)) % 123.27/123.51 (step @p212 :rule trans :premises (@p211 @p206)) % 123.27/123.51 (step @p213 :rule refl :args (@t242)) % 123.27/123.51 (step @p214 :rule refl :args (@t167)) % 123.27/123.51 (step @p215 :rule cong :premises (@p214 @p213) :args ((= @t167 @t242))) % 123.27/123.51 (step @p216 :rule symm :premises (@p215)) % 123.27/123.51 (step @p217 :rule eq_resolve :premises (@p214 @p216)) % 123.27/123.51 (step @p218 :rule cong :premises (@p217) :args (@t248)) % 123.27/123.51 (step @p219 :rule refl :args (@t243)) % 123.27/123.51 (step @p220 :rule refl :args (@t169)) % 123.27/123.51 (step @p221 :rule cong :premises (@p220 @p219) :args ((= @t169 @t243))) % 123.27/123.51 (step @p222 :rule symm :premises (@p221)) % 123.27/123.51 (step @p223 :rule eq_resolve :premises (@p220 @p222)) % 123.27/123.51 (step @p224 :rule cong :premises (@p223) :args (@t249)) % 123.27/123.51 (step @p225 :rule nary_cong :premises (@p224 @p218 @p212) :args (@t250)) % 123.27/123.51 (step @p226 :rule cong :premises (@p225) :args ((forall @t170 @t250))) % 123.27/123.51 (step @p227 :rule aci_norm :args ((= (or @t249 (or @t248 @t166)) @t250))) % 123.27/123.51 (step @p228 :rule bool-impl-elim :args (@t167 @t166)) % 123.27/123.51 (step @p229 :rule refl :args (@t249)) % 123.27/123.51 (step @p230 :rule nary_cong :premises (@p229 @p228) :args ((or @t249 @t168))) % 123.27/123.51 (step @p231 :rule trans :premises (@p230 @p227)) % 123.27/123.51 (step @p232 :rule bool-impl-elim :args (@t169 @t168)) % 123.27/123.51 (step @p233 :rule trans :premises (@p232 @p231)) % 123.27/123.51 (step @p234 :rule cong :premises (@p233) :args (@t171)) % 123.27/123.51 (step @p235 :rule trans :premises (@p234 @p226)) % 123.27/123.51 (step @p236 :rule refl :args ((_ @t51 @t172))) % 123.27/123.51 (step @p237 :rule refl :args (@t187)) % 123.27/123.51 (step @p238 :rule cong :premises (@p237) :args (@t188)) % 123.27/123.51 (step @p239 :rule trans :premises (@p238 @p236)) % 123.27/123.51 (step @p240 :rule ho_cong :premises (@p123 @p237)) % 123.27/123.51 (step @p241 :rule cong :premises (@p240 @p239) :args ((= (_ @t51 @t187) @t188))) % 123.27/123.51 (step @p242 :rule symm :premises (@p241)) % 123.27/123.51 (step @p243 :rule refl :args (@t173)) % 123.27/123.51 (step @p244 :rule eq_resolve :premises (@p243 @p242)) % 123.27/123.51 (step @p245 :rule refl :args (@t172)) % 123.27/123.51 (step @p246 :rule cong :premises (@p245 @p237) :args ((= @t172 @t187))) % 123.27/123.51 (step @p247 :rule symm :premises (@p246)) % 123.27/123.51 (step @p248 :rule eq_resolve :premises (@p245 @p247)) % 123.27/123.51 (step @p249 :rule ho_cong :premises (@p123 @p248)) % 123.27/123.51 (step @p250 :rule trans :premises (@p249 @p244)) % 123.27/123.51 (step @p251 :rule refl :args (@t189)) % 123.27/123.51 (step @p252 :rule refl :args (@t98)) % 123.27/123.51 (step @p253 :rule cong :premises (@p252 @p251) :args ((= @t98 @t189))) % 123.27/123.51 (step @p254 :rule symm :premises (@p253)) % 123.27/123.51 (step @p255 :rule eq_resolve :premises (@p252 @p254)) % 123.27/123.51 (step @p256 :rule cong :premises (@p255) :args (@t99)) % 123.27/123.51 (step @p257 :rule nary_cong :premises (@p256 @p250) :args (@t251)) % 123.27/123.51 (step @p258 :rule cong :premises (@p257) :args ((forall @t42 @t251))) % 123.27/123.51 (step @p259 :rule bool-impl-elim :args (@t98 @t173)) % 123.27/123.51 (step @p260 :rule cong :premises (@p259) :args (@t174)) % 123.27/123.51 (step @p261 :rule trans :premises (@p260 @p258)) % 123.27/123.51 (step @p262 :rule cong :premises (@p261 @p235) :args (@t175)) % 123.27/123.51 (step @p263 :rule refl :args (@t176)) % 123.27/123.51 (step @p264 :rule cong :premises (@p263 @p262) :args (@t177)) % 123.27/123.51 (step @p265 :rule cong :premises (@p264) :args (@t178)) % 123.27/123.51 (step @p266 :rule trans :premises (@p265 @p196)) % 123.27/123.51 (step @p267 :rule refl :args (tptp.pushprop_lem2v2)) % 123.27/123.51 (step @p268 :rule cong :premises (@p267 @p266) :args (@t179)) % 123.27/123.51 (step @p269 :rule cong :premises (@p268) :args (@t180)) % 123.27/123.51 (step @p270 :rule trans :premises (@p269 @p165)) % 123.27/123.51 (step @p271 :rule eq_resolve :premises (@p2 @p270)) % 123.27/123.51 (step @p272 :rule skolemize :premises (@p271)) % 123.27/123.51 (step @p273 :rule bool-double-not-elim :args (@t218)) % 123.27/123.51 (step @p274 :rule refl :args (@t256)) % 123.27/123.51 (step @p275 :rule nary_cong :premises (@p274 @p273) :args ((or @t256 (not @t253)))) % 123.27/123.51 (step @p276 :rule cnf_or_neg :args (@t256 2)) % 123.27/123.51 (step @p277 :rule eq_resolve :premises (@p276 @p275)) % 123.27/123.51 (step @p278 :rule reordering :premises (@p277) :args ((or @t218 @t256))) % 123.27/123.51 (step @p279 :rule chain_m_resolution :premises (@p278 @p272) :args (@t218 @t217 (@list @t256))) % 123.27/123.51 (step @p280 :rule true_intro :premises (@p279)) % 123.27/123.51 (step @p281 :rule symm :premises (@p280)) % 123.27/123.51 (step @p282 :rule trans :premises (@p281 @p78 @p25)) % 123.27/123.51 (step @p283 false :rule eq_resolve :premises (@p282 @p4)) % 123.27/123.51 ) % 123.27/123.51 % SZS output end Proof % 123.27/123.51 % cvc5 exiting %------------------------------------------------------------------------------