TSTP Solution File: SET814+4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 14:40:26 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 12:32:56 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.64 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.rxq0DSJYWc/cvc5---1.0.5_7051.p...
% 0.21/0.64 ------- get file name : TPTP file name is SET814+4
% 0.21/0.64 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7051.smt2...
% 0.21/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.64 % SZS status Theorem for SET814+4
% 0.21/0.64 % SZS output start Proof for SET814+4
% 0.21/0.64 (
% 0.21/0.64 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.member A tptp.on) (tptp.subset (tptp.sum A) A)))))) (let ((_let_2 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X A)))))))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_5 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (not _let_7))) (let ((_let_9 (or _let_8 _let_6))) (let ((_let_10 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (= _let_10 _let_5))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_14 (_let_12))) (let ((_let_15 ((tptp.subset A B)))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_10))) (let ((_let_19 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_20 (and (tptp.set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.strict_well_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_19))) (let ((_let_21 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on))) (let ((_let_22 (= _let_21 _let_20))) (let ((_let_23 (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_24 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_26 (tptp.subset _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (not _let_21))) (let ((_let_28 (or _let_27 _let_26))) (let ((_let_29 (forall ((A $$unsorted)) (or (not (tptp.member A tptp.on)) (tptp.subset (tptp.sum A) A))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) _let_31 :args (_let_30 true _let_29)))) (let ((_let_35 (_let_19))) (let ((_let_36 (or _let_17 _let_8))) (let ((_let_37 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (not _let_37))) (let ((_let_40 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_25))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y A)) (not (tptp.member X Y))))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (not _let_40))) (let ((_let_45 (or _let_44 _let_6))) (let ((_let_46 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (= _let_26 _let_46))) (let ((_let_49 (not _let_46))) (let ((_let_50 (_let_49))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_46))) (REFL :args (_let_47)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_48)) :args ((or _let_26 _let_49 (not _let_48)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 1)) _let_34 :args ((not _let_26) true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (_let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_15)) :args _let_14)) _let_13 :args (_let_48 false _let_12)) :args (_let_49 true _let_26 false _let_48)) :args (_let_47 true _let_46)))) (let ((_let_52 (_let_39))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_37))) (REFL :args (_let_38)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_41)) :args ((or _let_44 _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_40))) :args _let_32)) :args ((or _let_40 _let_45))) _let_51 :args (_let_40 true _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.member X (tptp.sum A))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_39 false _let_40 false _let_41)) :args (_let_38 true _let_37)))) (let ((_let_54 (REFL :args (_let_36)))) (let ((_let_55 (not _let_9))) (let ((_let_56 (_let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_56) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_9)) :args ((or _let_6 _let_8 _let_55))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 1)) _let_51 :args ((not _let_6) true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 1)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_32)) :args ((or _let_7 _let_36))) _let_53 :args (_let_7 true _let_36)) :args (_let_55 true _let_6 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or (not _let_10) _let_5 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_17 _let_10 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_32)) :args ((or _let_16 _let_36))) _let_53 :args (_let_16 true _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_35) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 2)) :args ((or _let_19 (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_22)) :args ((or _let_27 _let_20 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_21))) :args _let_32)) :args ((or _let_21 _let_28))) _let_34 :args (_let_21 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.member A tptp.on)))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_20 false _let_21 false _let_22)) :args (_let_19 false _let_20)) :args (_let_18 false _let_19)) :args (_let_10 false _let_16 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_15)) :args _let_14)) _let_13 :args (_let_11 false _let_12)) :args (_let_5 false _let_10 false _let_11)) :args (false true _let_9 false _let_5)) :args (_let_4 (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 $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) _let_3 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_2 (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 $$unsorted)) (tptp.least Y R A))))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (or (= M X) (tptp.apply R M X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply tptp.member_predicate X Y) (tptp.member X Y))) (forall ((R $$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))))))) (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))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.64 )
% 0.21/0.64 % SZS output end Proof for SET814+4
% 0.21/0.65 % cvc5---1.0.5 exiting
% 0.21/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------