%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL843-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:24:01 AM UTC 2026 % Result : Unsatisfiable 0.22s 0.49s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL843-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.11/0.36 % Computer : n008.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Fri Sep 4 18:52:38 UTC 2026 % 0.15/0.36 % CPUTime : % 0.15/0.44 %----Proving TF0_NAR, FOF, or CNF % 0.15/0.46 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.22/0.49 % SZS status Unsatisfiable % 0.22/0.49 % SZS output start Proof % 0.22/0.49 ( % 0.22/0.49 (declare-sort $$unsorted 0) % 0.22/0.49 (declare-const tptp.c_InductTermi_OIT (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.v_Ta______ $$unsorted) % 0.22/0.49 (declare-const tptp.v_x______ $$unsorted) % 0.22/0.49 (declare-const tptp.c_Lambda_OdB_OApp (-> $$unsorted $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.c_Lambda_Osubst (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.c_Lambda_OdB_OVar (-> $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.v_env______ (-> $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.c_Lambda_Olift (-> $$unsorted $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.c_Lambda_Osko__Lambda__Xbeta__cases__2__1 (-> $$unsorted $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.class_Orderings_Oorder (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.class_Ring__and__Field_Oordered__idom (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.c_Nat_Osemiring__1__class_Oof__nat (-> $$unsorted $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.c_HOL_Oord__class_Oless (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.c_Lambda_OdB_OAbs (-> $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.class_Ring__and__Field_Oordered__semidom (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.tc_nat $$unsorted) % 0.22/0.49 (declare-const tptp.class_Nat_Osemiring__char__0 (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.class_Ring__and__Field_Osemiring__1 (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.class_Orderings_Opreorder (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.c_HOL_Ozero__class_Ozero (-> $$unsorted $$unsorted)) % 0.22/0.49 (declare-const tptp.class_Orderings_Olinorder (-> $$unsorted Bool)) % 0.22/0.49 (declare-const tptp.c_Lambda_Obeta (-> $$unsorted $$unsorted Bool)) % 0.22/0.49 (define @t1 () (@var "T_a" $$unsorted)) % 0.22/0.49 (define @t2 () (tptp.c_HOL_Ozero__class_Ozero @t1)) % 0.22/0.49 (define @t3 () (@var "V_m" $$unsorted)) % 0.22/0.49 (define @t4 () (tptp.c_Nat_Osemiring__1__class_Oof__nat @t3 @t1)) % 0.22/0.49 (define @t5 () (not (tptp.class_Ring__and__Field_Oordered__semidom @t1))) % 0.22/0.49 (define @t6 () (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) % 0.22/0.49 (define @t7 () (@var "V_n" $$unsorted)) % 0.22/0.49 (define @t8 () (= @t3 @t7)) % 0.22/0.49 (define @t9 () (tptp.c_Nat_Osemiring__1__class_Oof__nat @t7 @t1)) % 0.22/0.49 (define @t10 () (@list @t1 @t3 @t7)) % 0.22/0.49 (define @t11 () (tptp.c_HOL_Oord__class_Oless @t3 @t7 tptp.tc_nat)) % 0.22/0.49 (define @t12 () (tptp.c_HOL_Oord__class_Oless @t4 @t9 @t1)) % 0.22/0.49 (define @t13 () (@var "V_b" $$unsorted)) % 0.22/0.49 (define @t14 () (@var "V_a" $$unsorted)) % 0.22/0.49 (define @t15 () (not (tptp.c_HOL_Oord__class_Oless @t14 @t13 @t1))) % 0.22/0.49 (define @t16 () (not (tptp.c_HOL_Oord__class_Oless @t13 @t14 @t1))) % 0.22/0.49 (define @t17 () (not (tptp.class_Orderings_Opreorder @t1))) % 0.22/0.49 (define @t18 () (@var "V_y" $$unsorted)) % 0.22/0.49 (define @t19 () (@var "V_x" $$unsorted)) % 0.22/0.49 (define @t20 () (tptp.c_HOL_Oord__class_Oless @t19 @t18 @t1)) % 0.22/0.49 (define @t21 () (not @t20)) % 0.22/0.49 (define @t22 () (tptp.c_HOL_Oord__class_Oless @t18 @t19 @t1)) % 0.22/0.49 (define @t23 () (not @t22)) % 0.22/0.49 (define @t24 () (@list @t1 @t18 @t19)) % 0.22/0.49 (define @t25 () (not (tptp.class_Orderings_Olinorder @t1))) % 0.22/0.49 (define @t26 () (@list @t1 @t19 @t18)) % 0.22/0.49 (define @t27 () (not (tptp.class_Orderings_Oorder @t1))) % 0.22/0.49 (define @t28 () (tptp.c_HOL_Oord__class_Oless @t6 @t7 tptp.tc_nat)) % 0.22/0.49 (define @t29 () (@list @t7)) % 0.22/0.49 (define @t30 () (tptp.c_HOL_Oord__class_Oless @t2 @t9 @t1)) % 0.22/0.49 (define @t31 () (@list @t1 @t7)) % 0.22/0.49 (define @t32 () (= @t19 @t18)) % 0.22/0.49 (define @t33 () (not (tptp.c_HOL_Oord__class_Oless @t19 @t19 @t1))) % 0.22/0.49 (define @t34 () (@list @t1 @t19)) % 0.22/0.49 (define @t35 () (tptp.c_HOL_Oord__class_Oless @t19 @t19 tptp.tc_nat)) % 0.22/0.49 (define @t36 () (@var "V_z" $$unsorted)) % 0.22/0.49 (define @t37 () (@var "V_t" $$unsorted)) % 0.22/0.49 (define @t38 () (@var "V_s" $$unsorted)) % 0.22/0.49 (define @t39 () (not (tptp.c_Lambda_Obeta @t38 @t37))) % 0.22/0.49 (define @t40 () (tptp.c_Lambda_OdB_OAbs @t38)) % 0.22/0.49 (define @t41 () (@list @t38 @t37)) % 0.22/0.49 (define @t42 () (@var "V_r" $$unsorted)) % 0.22/0.49 (define @t43 () (tptp.c_Lambda_OdB_OAbs @t42)) % 0.22/0.49 (define @t44 () (not (tptp.c_Lambda_Obeta @t43 @t38))) % 0.22/0.49 (define @t45 () (tptp.c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @t42 @t38)) % 0.22/0.49 (define @t46 () (not (tptp.c_Lambda_Obeta @t42 @t38))) % 0.22/0.49 (define @t47 () (@var "V_i" $$unsorted)) % 0.22/0.49 (define @t48 () (@var "V_k" $$unsorted)) % 0.22/0.49 (define @t49 () (tptp.c_Lambda_OdB_OVar @t47)) % 0.22/0.49 (define @t50 () (tptp.c_Lambda_Olift @t37 @t48)) % 0.22/0.49 (define @t51 () (@var "V_u" $$unsorted)) % 0.22/0.49 (define @t52 () (tptp.c_Lambda_OdB_OApp @t37 @t51)) % 0.22/0.49 (define @t53 () (@var "V_dB_H" $$unsorted)) % 0.22/0.49 (define @t54 () (@var "V_dB" $$unsorted)) % 0.22/0.49 (define @t55 () (tptp.c_Lambda_OdB_OAbs @t53)) % 0.22/0.49 (define @t56 () (@var "V_dB2_H" $$unsorted)) % 0.22/0.49 (define @t57 () (@var "V_dB2" $$unsorted)) % 0.22/0.49 (define @t58 () (@var "V_dB1_H" $$unsorted)) % 0.22/0.49 (define @t59 () (tptp.c_Lambda_OdB_OApp @t58 @t56)) % 0.22/0.49 (define @t60 () (@var "V_dB1" $$unsorted)) % 0.22/0.49 (define @t61 () (tptp.c_Lambda_OdB_OApp @t60 @t57)) % 0.22/0.49 (define @t62 () (not (= @t61 @t59))) % 0.22/0.49 (define @t63 () (@list @t60 @t57 @t58 @t56)) % 0.22/0.49 (define @t64 () (@var "V_j" $$unsorted)) % 0.22/0.49 (define @t65 () (tptp.c_Lambda_OdB_OVar @t64)) % 0.22/0.49 (define @t66 () (@var "V_nat" $$unsorted)) % 0.22/0.49 (define @t67 () (tptp.c_Lambda_OdB_OVar @t66)) % 0.22/0.49 (define @t68 () (@var "V_nat_H" $$unsorted)) % 0.22/0.49 (define @t69 () (not (tptp.c_InductTermi_OIT @t42))) % 0.22/0.49 (define @t70 () (not (tptp.c_InductTermi_OIT @t37))) % 0.22/0.49 (define @t71 () (@list @t37 @t47)) % 0.22/0.49 (define @t72 () (forall @t29 (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar @t7)))) % 0.22/0.49 (define @t73 () (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar tptp.v_x______))) % 0.22/0.49 (assume @p1 (forall (@list @t1 @t3) (or @t5 (not (tptp.c_HOL_Oord__class_Oless @t4 @t2 @t1))))) % 0.22/0.49 (assume @p2 (forall (@list @t1) (or (not (tptp.class_Ring__and__Field_Osemiring__1 @t1)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat @t6 @t1) @t2)))) % 0.22/0.49 (assume @p3 (forall @t10 (or (not (tptp.class_Nat_Osemiring__char__0 @t1)) (not (= @t4 @t9)) @t8))) % 0.22/0.49 (assume @p4 (forall @t10 (or @t5 @t12 (not @t11)))) % 0.22/0.49 (assume @p5 (forall @t10 (or @t5 @t11 (not @t12)))) % 0.22/0.49 (assume @p6 (forall (@list @t1 @t13 @t14) (or @t17 @t16 @t15))) % 0.22/0.49 (assume @p7 (forall @t24 (or @t17 @t23 @t21))) % 0.22/0.49 (assume @p8 (forall @t26 (or @t25 @t21 @t23))) % 0.22/0.49 (assume @p9 (forall (@list @t1 @t14 @t13) (or @t27 @t15 @t16))) % 0.22/0.49 (assume @p10 (not (tptp.c_HOL_Oord__class_Oless @t6 @t6 tptp.tc_nat))) % 0.22/0.49 (assume @p11 (forall @t29 (or @t28 (= @t7 @t6)))) % 0.22/0.49 (assume @p12 (forall @t31 (or @t5 @t28 (not @t30)))) % 0.22/0.49 (assume @p13 (forall @t31 (or @t5 @t30 (not @t28)))) % 0.22/0.49 (assume @p14 (forall @t26 (or @t25 @t32 @t20 @t22))) % 0.22/0.49 (assume @p15 (forall @t24 (or @t25 @t22 @t32 @t20))) % 0.22/0.49 (assume @p16 (forall @t24 (or @t25 @t22 @t20 @t32))) % 0.22/0.49 (assume @p17 (forall (@list @t18 @t19) (or (tptp.c_HOL_Oord__class_Oless @t18 @t19 tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless @t19 @t18 tptp.tc_nat) @t32))) % 0.22/0.49 (assume @p18 (forall (@list @t7 @t3) (or (tptp.c_HOL_Oord__class_Oless @t7 @t3 tptp.tc_nat) @t11 @t8))) % 0.22/0.49 (assume @p19 (forall @t26 (or @t25 @t32 @t22 @t20))) % 0.22/0.49 (assume @p20 (forall @t24 (or (not (tptp.class_Ring__and__Field_Oordered__idom @t1)) @t22 @t20 @t32))) % 0.22/0.49 (assume @p21 (forall @t34 (or @t17 @t33))) % 0.22/0.49 (assume @p22 (forall @t34 (or @t25 @t33))) % 0.22/0.49 (assume @p23 (forall @t34 (or @t27 @t33))) % 0.22/0.49 (assume @p24 (forall @t29 (not (tptp.c_HOL_Oord__class_Oless @t7 @t7 tptp.tc_nat)))) % 0.22/0.49 (assume @p25 (forall (@list @t19) (not @t35))) % 0.22/0.49 (assume @p26 (forall (@list @t1 @t19 @t36 @t18) (or @t17 (tptp.c_HOL_Oord__class_Oless @t19 @t36 @t1) (not (tptp.c_HOL_Oord__class_Oless @t18 @t36 @t1)) @t21))) % 0.22/0.49 (assume @p27 (forall (@list @t1 @t36 @t19 @t18) (or @t27 (tptp.c_HOL_Oord__class_Oless @t36 @t19 @t1) (not (tptp.c_HOL_Oord__class_Oless @t36 @t18 @t1)) @t23))) % 0.22/0.49 (assume @p28 (forall (@list @t3) (not (tptp.c_HOL_Oord__class_Oless @t3 @t6 tptp.tc_nat)))) % 0.22/0.49 (assume @p29 (forall @t29 (not (tptp.c_HOL_Oord__class_Oless @t7 @t6 tptp.tc_nat)))) % 0.22/0.49 (assume @p30 (forall @t41 (or (tptp.c_Lambda_Obeta @t40 (tptp.c_Lambda_OdB_OAbs @t37)) @t39))) % 0.22/0.49 (assume @p31 (forall (@list @t38 @t42) (or (= @t38 (tptp.c_Lambda_OdB_OAbs @t45)) @t44))) % 0.22/0.49 (assume @p32 (forall (@list @t42 @t47 @t38) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_Olift @t42 @t47) (tptp.c_Lambda_Olift @t38 @t47)) @t46))) % 0.22/0.49 (assume @p33 (forall (@list @t47 @t48) (or (= (tptp.c_Lambda_Olift @t49 @t48) @t49) (not (tptp.c_HOL_Oord__class_Oless @t47 @t48 tptp.tc_nat))))) % 0.22/0.49 (assume @p34 (forall (@list @t37 @t48 @t38) (= (tptp.c_Lambda_Osubst @t50 @t38 @t48) @t37))) % 0.22/0.49 (assume @p35 (forall (@list @t38 @t51 @t37) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OApp @t38 @t51) @t52) @t39))) % 0.22/0.49 (assume @p36 (forall (@list @t51 @t38 @t37) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OApp @t51 @t38) (tptp.c_Lambda_OdB_OApp @t51 @t37)) @t39))) % 0.22/0.50 (assume @p37 (forall (@list @t19 @t38) (or @t35 (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar @t19) @t38 @t19) @t38)))) % 0.22/0.50 (assume @p38 (forall (@list @t47 @t38 @t48) (or (= (tptp.c_Lambda_Osubst @t49 @t38 @t48) @t49) (= @t47 @t48) (tptp.c_HOL_Oord__class_Oless @t48 @t47 tptp.tc_nat)))) % 0.22/0.50 (assume @p39 (forall (@list @t42 @t37 @t47 @t38) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_Osubst @t42 @t37 @t47) (tptp.c_Lambda_Osubst @t38 @t37 @t47)) @t46))) % 0.22/0.50 (assume @p40 (forall (@list @t38 @t37 @t48) (= (tptp.c_Lambda_Olift (tptp.c_Lambda_OdB_OApp @t38 @t37) @t48) (tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift @t38 @t48) @t50)))) % 0.22/0.50 (assume @p41 (forall (@list @t54 @t53) (or (not (= (tptp.c_Lambda_OdB_OAbs @t54) @t55)) (= @t54 @t53)))) % 0.22/0.50 (assume @p42 (forall @t41 (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OApp @t40 @t37) (tptp.c_Lambda_Osubst @t38 @t37 @t6)))) % 0.22/0.50 (assume @p43 (forall @t63 (or @t62 (= @t57 @t56)))) % 0.22/0.50 (assume @p44 (forall @t63 (or @t62 (= @t60 @t58)))) % 0.22/0.50 (assume @p45 (forall (@list @t42 @t38) (or (tptp.c_Lambda_Obeta @t42 @t45) @t44))) % 0.22/0.50 (assume @p46 (forall (@list @t64 @t51 @t47) (or (= (tptp.c_Lambda_Osubst @t65 @t51 @t47) @t65) (not (tptp.c_HOL_Oord__class_Oless @t64 @t47 tptp.tc_nat))))) % 0.22/0.50 (assume @p47 (forall (@list @t53 @t60 @t57) (not (= @t55 @t61)))) % 0.22/0.50 (assume @p48 (forall (@list @t60 @t57 @t53) (not (= @t61 @t55)))) % 0.22/0.50 (assume @p49 (forall (@list @t37 @t51 @t38 @t48) (= (tptp.c_Lambda_Osubst @t52 @t38 @t48) (tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst @t37 @t38 @t48) (tptp.c_Lambda_Osubst @t51 @t38 @t48))))) % 0.22/0.50 (assume @p50 (forall (@list @t53 @t66) (not (= @t55 @t67)))) % 0.22/0.50 (assume @p51 (forall (@list @t66 @t68) (or (not (= @t67 (tptp.c_Lambda_OdB_OVar @t68))) (= @t66 @t68)))) % 0.22/0.50 (assume @p52 (forall (@list @t48 @t51) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar @t48) @t51 @t48) @t51))) % 0.22/0.50 (assume @p53 (= (tptp.v_env______ tptp.v_x______) tptp.v_Ta______)) % 0.22/0.50 (assume @p54 (forall (@list @t42 @t47 @t64) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst @t42 @t49 @t64)) @t69))) % 0.22/0.50 (assume @p55 (forall (@list @t47 @t37) (not (tptp.c_Lambda_Obeta @t49 @t37)))) % 0.22/0.50 (assume @p56 (forall (@list @t66 @t58 @t56) (not (= @t67 @t59)))) % 0.22/0.50 (assume @p57 (forall @t71 (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift @t37 @t47)) @t70))) % 0.22/0.50 (assume @p58 (forall (@list @t66 @t53) (not (= @t67 @t55)))) % 0.22/0.50 (assume @p59 @t72) % 0.22/0.50 (assume @p60 (forall (@list @t42) (or (tptp.c_InductTermi_OIT @t43) @t69))) % 0.22/0.50 (assume @p61 (forall @t71 (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OApp @t37 @t49)) @t70))) % 0.22/0.50 (assume @p62 (forall (@list @t58 @t56 @t66) (not (= @t59 @t67)))) % 0.22/0.50 (assume @p63 (not @t73)) % 0.22/0.50 (assume @p64 (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat)) % 0.22/0.50 (assume @p65 (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat)) % 0.22/0.50 (assume @p66 (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat)) % 0.22/0.50 (assume @p67 (tptp.class_Orderings_Opreorder tptp.tc_nat)) % 0.22/0.50 (assume @p68 (tptp.class_Orderings_Olinorder tptp.tc_nat)) % 0.22/0.50 (assume @p69 (tptp.class_Orderings_Oorder tptp.tc_nat)) % 0.22/0.50 (assume-push @p77 @t72) % 0.22/0.50 (step @p71 :rule instantiate :premises (@p59) :args ((@list tptp.v_x______))) % 0.22/0.50 (step-pop @p78 :rule scope :premises (@p71)) % 0.22/0.50 (step @p72 :rule process_scope :premises (@p78) :args (@t73)) % 0.22/0.50 (step @p74 :rule implies_elim :premises (@p72)) % 0.22/0.50 (step @p75 :rule reordering :premises (@p74) :args ((or @t73 (not @t72)))) % 0.22/0.50 (step @p76 false :rule chain_m_resolution :premises (@p75 @p63 @p59) :args (false (@list true false) (@list @t73 @t72))) % 0.22/0.50 ) % 0.22/0.50 % SZS output end Proof % 0.22/0.50 % cvc5 exiting %------------------------------------------------------------------------------