TSTP Solution File: SET800+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET800+4 : 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 14:40:23 EDT 2023
% Result : Theorem 0.23s 0.58s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 09:30:26 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.23/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dEv1S2E4iR/cvc5---1.0.5_10368.p...
% 0.23/0.58 ------- get file name : TPTP file name is SET800+4
% 0.23/0.58 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10368.smt2...
% 0.23/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.58 % SZS status Theorem for SET800+4
% 0.23/0.58 % SZS output start Proof for SET800+4
% 0.23/0.58 (
% 0.23/0.58 (let ((_let_1 (not (forall ((R $$unsorted) (E $$unsorted)) (=> (tptp.order R E) (forall ((X1 $$unsorted) (X2 $$unsorted)) (=> (and (tptp.subset X1 E) (tptp.subset X2 E) (tptp.subset X1 X2)) (forall ((M1 $$unsorted) (M2 $$unsorted)) (=> (and (tptp.greatest_lower_bound M1 X1 R E) (tptp.greatest_lower_bound M2 X2 R E)) (tptp.apply R M2 M1)))))))))) (let ((_let_2 (forall ((A $$unsorted) (X $$unsorted) (R $$unsorted) (E $$unsorted)) (= (tptp.greatest_lower_bound A X R E) (and (tptp.member A X) (tptp.lower_bound A R X) (forall ((M $$unsorted)) (=> (and (tptp.member M E) (tptp.lower_bound M R X)) (tptp.apply R M A)))))))) (let ((_let_3 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.lower_bound M R E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R M X))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_5 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X))))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (not _let_7))) (let ((_let_9 (or _let_8 _let_6))) (let ((_let_10 (tptp.lower_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_11 (= _let_10 _let_5))) (let ((_let_12 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.lower_bound M R E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R M X))))))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_14 (and (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_10 (forall ((M $$unsorted)) (or (not (tptp.member M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.lower_bound M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_15 (tptp.greatest_lower_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (forall ((A $$unsorted) (X $$unsorted) (R $$unsorted) (E $$unsorted)) (= (tptp.greatest_lower_bound A X R E) (and (tptp.member A X) (tptp.lower_bound A R X) (forall ((M $$unsorted)) (or (not (tptp.member M E)) (not (tptp.lower_bound M R X)) (tptp.apply R M A)))))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 ((tptp.greatest_lower_bound A X R E)))) (let ((_let_21 (not _let_15))) (let ((_let_22 (tptp.greatest_lower_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or (not (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_25 _let_23 _let_21 _let_6))) (let ((_let_27 (forall ((R $$unsorted) (E $$unsorted) (BOUND_VARIABLE_1097 $$unsorted) (BOUND_VARIABLE_1095 $$unsorted) (BOUND_VARIABLE_1093 $$unsorted) (BOUND_VARIABLE_1091 $$unsorted)) (or (not (tptp.order R E)) (not (tptp.subset BOUND_VARIABLE_1091 E)) (not (tptp.subset BOUND_VARIABLE_1093 E)) (not (tptp.subset BOUND_VARIABLE_1091 BOUND_VARIABLE_1093)) (not (tptp.greatest_lower_bound BOUND_VARIABLE_1097 BOUND_VARIABLE_1091 R E)) (not (tptp.greatest_lower_bound BOUND_VARIABLE_1095 BOUND_VARIABLE_1093 R E)) (tptp.apply R BOUND_VARIABLE_1095 BOUND_VARIABLE_1097))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (or))) (let ((_let_31 (not _let_27))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_29) :args (_let_31))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args (_let_28)) :args _let_30)) _let_29 :args (_let_28 true _let_27)))) (let ((_let_33 (REFL :args (_let_26)))) (let ((_let_34 (not _let_9))) (let ((_let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_7))) (let ((_let_38 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_39 (= _let_24 _let_38))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_38))) (let ((_let_43 (and _let_35 (tptp.lower_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) (forall ((M $$unsorted)) (or (not (tptp.member M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.lower_bound M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_44 (= _let_22 _let_43))) (let ((_let_45 (_let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_9)) :args ((or _let_6 _let_8 _let_34))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 6)) _let_32 :args ((not _let_6) true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_7 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_43 0)) :args ((or _let_35 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_23 _let_43 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 4)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_30)) :args ((or _let_22 _let_26))) _let_32 :args (_let_22 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_44 false _let_17)) :args (_let_43 false _let_22 false _let_44)) :args (_let_35 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false))))) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_25 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 3)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_30)) :args ((or _let_24 _let_26))) _let_32 :args (_let_24 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_38 false _let_24 false _let_39)) :args (_let_37 false _let_38)) :args (_let_7 false _let_35 false _let_37)) :args (_let_34 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_AND_POS :args (_let_14 1)) :args ((or _let_10 (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_16)) :args ((or _let_21 _let_14 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 5)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_15))) :args _let_30)) :args ((or _let_15 _let_26))) _let_32 :args (_let_15 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_16 false _let_17)) :args (_let_14 false _let_15 false _let_16)) :args (_let_10 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.lower_bound M R E)))) :args (_let_12))) _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 $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$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 $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y X)) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.total_order R E) (and (tptp.order R E) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (or (tptp.apply R X Y) (tptp.apply R Y X))))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.upper_bound M R E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M))))) _let_3 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.greatest M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M)))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R M X)))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.max M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R M X)) (= M X)))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.min M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R X M)) (= M X)))))) (forall ((A $$unsorted) (X $$unsorted) (R $$unsorted) (E $$unsorted)) (= (tptp.least_upper_bound A X R E) (and (tptp.member A X) (tptp.upper_bound A R X) (forall ((M $$unsorted)) (=> (and (tptp.member M E) (tptp.upper_bound M R X)) (tptp.apply R A M)))))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.59 )
% 0.23/0.59 % SZS output end Proof for SET800+4
% 0.23/0.59 % cvc5---1.0.5 exiting
% 0.23/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------