TSTP Solution File: NUM409+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 : Thu Aug 31 10:43:42 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:27:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.57 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.oNOkBGlOIr/cvc5---1.0.5_2049.p...
% 0.19/0.57 ------- get file name : TPTP file name is NUM409+1
% 0.19/0.57 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2049.smt2...
% 0.19/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.57 % SZS status Theorem for NUM409+1
% 0.19/0.57 % SZS output start Proof for NUM409+1
% 0.19/0.57 (
% 0.19/0.57 (let ((_let_1 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))))) (let ((_let_2 (forall ((A $$unsorted)) (tptp.transfinite_sequence_of tptp.empty_set A)))) (let ((_let_3 (not _let_2))) (let ((_let_4 (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)))) (let ((_let_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))))) (let ((_let_6 (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))))) (let ((_let_7 (tptp.relation tptp.empty_set))) (let ((_let_8 (tptp.empty tptp.empty_set))) (let ((_let_9 (tptp.function tptp.empty_set))) (let ((_let_10 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_11 (and _let_7 _let_10 _let_9 (tptp.one_to_one tptp.empty_set) _let_8 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)))) (let ((_let_12 (and _let_8 _let_7 _let_10))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B) (tptp.transfinite_sequence B)) (= (tptp.transfinite_sequence_of B A) (tptp.subset (tptp.relation_rng B) A)))))) (let ((_let_14 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.transfinite_sequence A) (tptp.ordinal (tptp.relation_dom A))))))) (let ((_let_15 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))))) (let ((_let_16 (tptp.relation_rng tptp.empty_set))) (let ((_let_17 (tptp.subset _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_18 (= tptp.empty_set _let_16))) (let ((_let_19 (tptp.subset tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_20 (tptp.transfinite_sequence_of tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_21 (= _let_20 _let_17))) (let ((_let_22 (not _let_17))) (let ((_let_23 (tptp.transfinite_sequence tptp.empty_set))) (let ((_let_24 (not _let_23))) (let ((_let_25 (not _let_9))) (let ((_let_26 (not _let_7))) (let ((_let_27 (or _let_26 _let_25 _let_24 _let_21))) (let ((_let_28 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.transfinite_sequence B)) (= (tptp.transfinite_sequence_of B A) (tptp.subset (tptp.relation_rng B) A)))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (tptp.relation_dom tptp.empty_set))) (let ((_let_31 (tptp.ordinal _let_30))) (let ((_let_32 (= _let_23 _let_31))) (let ((_let_33 (or _let_26 _let_25 _let_32))) (let ((_let_34 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (= (tptp.transfinite_sequence A) (tptp.ordinal (tptp.relation_dom A))))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (AND_ELIM (ASSUME :args (_let_11)) :args (2)))) (let ((_let_37 (ASSUME :args (_let_12)))) (let ((_let_38 (AND_ELIM _let_37 :args (1)))) (let ((_let_39 (and (tptp.epsilon_transitive _let_30) (tptp.epsilon_connected _let_30) _let_31))) (let ((_let_40 (tptp.empty _let_30))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39))) (let ((_let_43 (forall ((A $$unsorted)) (or (not (tptp.empty A)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (and _let_40 (tptp.relation _let_30)))) (let ((_let_46 (not _let_8))) (let ((_let_47 (or _let_46 _let_45))) (let ((_let_48 (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (or (not (tptp.empty A)) (and (tptp.empty _let_1) (tptp.relation _let_1))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (AND_ELIM _let_37 :args (0)))) (let ((_let_51 (not _let_20))) (let ((_let_52 (_let_3))) (let ((_let_53 (ASSUME :args _let_52))) (let ((_let_54 (or))) (let ((_let_55 (tptp.empty _let_16))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_18))) (let ((_let_58 (forall ((A $$unsorted)) (or (not (tptp.empty A)) (= tptp.empty_set A))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (and _let_55 (tptp.relation _let_16)))) (let ((_let_61 (or _let_46 _let_60))) (let ((_let_62 (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (or (not (tptp.empty A)) (and (tptp.empty _let_1) (tptp.relation _let_1))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (_let_4))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (not _let_19))) (let ((_let_67 (not _let_18))) (let ((_let_68 (ASSUME :args (_let_19)))) (let ((_let_69 (ASSUME :args (_let_18)))) (let ((_let_70 (ASSUME :args (_let_22)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_68 _let_69 _let_70) :args (_let_18 _let_22 _let_19)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_70)) (CONG (SYMM _let_69) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) :args (APPLY_UF tptp.subset)) (TRUE_INTRO _let_68))) :args (_let_19 _let_18 _let_22)) :args ((not (and _let_18 _let_22 _let_19)) SB_LITERAL))) (CONG (REFL :args (_let_67)) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_17))) (REFL :args (_let_66)) :args _let_54)) :args ((or _let_17 _let_67 _let_66))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset tptp.empty_set A) true))))) :args _let_64)) _let_65 :args (_let_19 false _let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_18 _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 0)) :args ((or _let_55 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_46 _let_60 (not _let_61)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_rng A)))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_60 false _let_8 false _let_61)) :args (_let_55 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty A) false))))) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_18 false _let_55 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_21)) :args ((or _let_20 _let_22 (not _let_21)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_53) :args _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) (REFL :args (_let_51)) :args _let_54)) _let_53 :args (_let_51 true _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_25 _let_24 _let_21 (not _let_27)))) _let_38 _let_36 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_32)) :args ((or _let_23 (not _let_31) (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 2)) :args ((or _let_31 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_39 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_40 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_45 (not _let_47)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_dom A)))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_45 false _let_8 false _let_47)) :args (_let_40 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_30 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordinal A)))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_39 false _let_40 false _let_42)) :args (_let_31 false _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_26 _let_25 _let_32 (not _let_33)))) _let_38 _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_32 false _let_7 false _let_9 false _let_33)) :args (_let_23 false _let_31 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.transfinite_sequence_of B A)))) :args (_let_28))) _let_29 :args (_let_27 false _let_28)) :args (_let_21 false _let_7 false _let_9 false _let_23 false _let_27)) :args (_let_22 true _let_20 false _let_21)) :args (false false _let_19 false _let_18 true _let_17)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) _let_15 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair C D) A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) _let_14 _let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.transfinite_sequence_of B A) (and (tptp.relation B) (tptp.function B) (tptp.transfinite_sequence B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.transfinite_sequence_of B A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) _let_12 _let_8 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) _let_11 (and _let_8 _let_7) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A)) (tptp.with_non_empty_elements (tptp.relation_rng A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))) _let_6 _let_5 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.58 )
% 0.19/0.58 % SZS output end Proof for NUM409+1
% 0.19/0.58 % cvc5---1.0.5 exiting
% 0.19/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------