TSTP Solution File: SET810+4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET810+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 14:40:25 EDT 2023
% Result : Theorem 0.21s 0.57s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET810+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 11:10:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ZwdwR6Uu3Q/cvc5---1.0.5_12468.p...
% 0.21/0.57 ------- get file name : TPTP file name is SET810+4
% 0.21/0.57 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12468.smt2...
% 0.21/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.57 % SZS status Theorem for SET810+4
% 0.21/0.57 % SZS output start Proof for SET810+4
% 0.21/0.57 (
% 0.21/0.57 (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.member A tptp.on) (tptp.member B tptp.on)) (not (and (tptp.member A B) (tptp.member B A)))))))) (let ((_let_2 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (not (and (tptp.apply R X Y) (tptp.apply R Y X))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply tptp.member_predicate X Y) (tptp.member X Y))))) (let ((_let_4 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted)) (=> (and (tptp.subset A E) (exists ((X $$unsorted)) (tptp.member X A))) (exists ((Y $$unsorted)) (tptp.least Y R A))))))))) (let ((_let_5 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X A)))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (not _let_9))) (let ((_let_11 (not _let_8))) (let ((_let_12 (not _let_7))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_11 _let_10))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.on)) _let_17 _let_12))) (let ((_let_21 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.member A tptp.on)) (not (tptp.member B tptp.on)) (not (tptp.member A B)) (not (tptp.member B A)))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (or))) (let ((_let_25 (not _let_21))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_23) :args (_let_25))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_21))) (REFL :args (_let_22)) :args _let_24)) _let_23 :args (_let_22 true _let_21)))) (let ((_let_27 (REFL :args (_let_20)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 3)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_7))) :args _let_24)) :args ((or _let_7 _let_20))) _let_26 :args (_let_7 true _let_20)))) (let ((_let_29 (= _let_16 _let_8))) (let ((_let_30 (_let_3))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 ((tptp.member X Y)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 2)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_24)) :args ((or _let_16 _let_20))) _let_26 :args (_let_16 true _let_20)))) (let ((_let_34 (= _let_7 _let_9))) (let ((_let_35 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y X)))))) (let ((_let_36 (and _let_35 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y Z)) (tptp.apply tptp.member_predicate X Z)))))) (let ((_let_37 (tptp.strict_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_38 (= _let_37 _let_36))) (let ((_let_39 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.member Z E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (and _let_37 (forall ((A $$unsorted) (BOUND_VARIABLE_897 $$unsorted)) (or (not (tptp.subset A SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member BOUND_VARIABLE_897 A)) (not (forall ((Y $$unsorted)) (not (tptp.least Y tptp.member_predicate A))))))))) (let ((_let_42 (tptp.strict_well_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (= _let_42 _let_41))) (let ((_let_44 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted) (BOUND_VARIABLE_897 $$unsorted)) (or (not (tptp.subset A E)) (not (tptp.member BOUND_VARIABLE_897 A)) (not (forall ((Y $$unsorted)) (not (tptp.least Y R A))))))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_47 (and (tptp.set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_42 _let_46))) (let ((_let_48 (= _let_18 _let_47))) (let ((_let_49 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.subset X A)))))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_48)) :args ((or _let_19 _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_24)) :args ((or _let_18 _let_20))) _let_26 :args (_let_18 true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.member A tptp.on)))) :args (_let_49))) _let_50 :args (_let_48 false _let_49)) :args (_let_47 false _let_18 false _let_48)))) (let ((_let_52 (not _let_47))) (let ((_let_53 (_let_35))) (let ((_let_54 (or _let_17 _let_13))) (let ((_let_55 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_56 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_57 (= _let_56 _let_55))) (let ((_let_58 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (or _let_12 _let_56))) (let ((_let_61 (_let_46))) (let ((_let_62 (_let_55))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_12 _let_11 _let_10 _let_14 (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_17 _let_13 (not _let_54)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_62) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_57)) :args ((or (not _let_56) _let_55 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_12 _let_56 (not _let_60)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 2)) :args ((or _let_46 _let_52))) _let_51 :args (_let_46 false _let_47)) :args (_let_60 false _let_46)) :args (_let_56 false _let_7 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_55 false _let_56 false _let_57)) :args (_let_54 false _let_55)) :args (_let_13 false _let_16 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_53) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply tptp.member_predicate X Y) false))))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 0)) :args ((or _let_35 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_38)) :args ((or (not _let_37) _let_36 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 0)) :args ((or _let_37 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or (not _let_42) _let_41 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 1)) :args ((or _let_42 _let_52))) _let_51 :args (_let_42 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.strict_well_order R E)))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_41 false _let_42 false _let_43)) :args (_let_37 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.strict_order R E)))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_36 false _let_37 false _let_38)) :args (_let_35 false _let_36)) :args (_let_15 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_34)) :args ((or _let_12 _let_9 (not _let_34)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_30))) _let_31 :args (_let_34 false _let_3)) :args (_let_9 false _let_7 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_29)) :args ((or _let_17 _let_8 (not _let_29)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_30))) _let_31 :args (_let_29 false _let_3)) :args (_let_8 false _let_16 false _let_29)) _let_28 :args (false false _let_13 false _let_15 false _let_9 false _let_8 false _let_7)) :args (_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_5 _let_4 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (or (= M X) (tptp.apply R M X))))))) _let_3 _let_2 (forall ((X $$unsorted)) (=> (tptp.set X) (forall ((Y $$unsorted)) (=> (tptp.member Y X) (tptp.set Y))))) (forall ((X $$unsorted) (R $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.initial_segment X R A)) (and (tptp.member Y A) (tptp.apply R Y X)))) (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.suc A)) (tptp.member X (tptp.union A (tptp.singleton A))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.58 )
% 0.21/0.58 % SZS output end Proof for SET810+4
% 0.21/0.58 % cvc5---1.0.5 exiting
% 0.21/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------