TSTP Solution File: SEU311+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU311+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 16:30:49 EDT 2023
% Result : Theorem 66.40s 66.58s
% Output : Proof 66.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU311+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:47:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 66.40/66.58 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.mlsRV6yuH5/cvc5---1.0.5_1535.p...
% 66.40/66.58 ------- get file name : TPTP file name is SEU311+1
% 66.40/66.58 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1535.smt2...
% 66.40/66.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 66.40/66.58 --- Run --no-e-matching --full-saturate-quant at 5...
% 66.40/66.58 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 66.40/66.58 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 66.40/66.58 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 66.40/66.58 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 66.40/66.58 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 66.40/66.58 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 66.40/66.58 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 66.40/66.58 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 66.40/66.58 --- Run --relevant-triggers --full-saturate-quant at 5...
% 66.40/66.58 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 66.40/66.58 % SZS status Theorem for SEU311+1
% 66.40/66.58 % SZS output start Proof for SEU311+1
% 66.40/66.58 (
% 66.40/66.58 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.element B A))) (let ((_let_2 (tptp.empty A))) (and (=> (not _let_2) (= _let_1 (tptp.in B A))) (=> _let_2 (= _let_1 (tptp.empty B))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.powerset (tptp.the_carrier A))) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B))))))))) (let ((_let_4 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))))) (let ((_let_5 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (exists ((C $$unsorted)) (and (tptp.element C (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier A))) (= (tptp.in D C) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B))))))))))) (let ((_let_6 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_7 (io_tptp.powerset_3 _let_6))) (let ((_let_8 (io_tptp.empty_13 _let_7))) (let ((_let_9 (io_tptp.in_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_150 _let_7))) (let ((_let_10 (io_tptp.element_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_150 _let_7))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (or _let_8 _let_11))) (let ((_let_13 (forall ((b_A it_3_$$unsorted)) (not (io_tptp.empty_13 (io_tptp.powerset_3 b_A)))))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_13)))))) (let ((_let_15 (not _let_11))) (let ((_let_16 (io_tptp.cast_as_carrier_subset_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_17 (io_tptp.in_5 (io_tptp.set_difference_7 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_150) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_18 (not _let_9))) (let ((_let_19 (io_tptp.in_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_150 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71))) (let ((_let_20 (= _let_17 _let_19))) (let ((_let_21 (and _let_9 _let_17))) (let ((_let_22 (= _let_19 _let_21))) (let ((_let_23 (not _let_10))) (let ((_let_24 (or _let_23 _let_20))) (let ((_let_25 (forall ((b_D it_3_$$unsorted)) (or (not (io_tptp.element_4 b_D (io_tptp.powerset_3 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22)))) (= (io_tptp.in_5 (io_tptp.set_difference_7 (io_tptp.cast_as_carrier_subset_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) b_D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) (io_tptp.in_5 b_D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71)))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (not _let_25))) (let ((_let_28 (io_tptp.powerset_3 _let_7))) (let ((_let_29 (io_tptp.element_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 _let_28))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_27))) (let ((_let_32 (forall ((b_C it_3_$$unsorted)) (or (not (io_tptp.element_4 b_C (io_tptp.powerset_3 (io_tptp.powerset_3 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))))) (not (forall ((b_D it_3_$$unsorted)) (or (not (io_tptp.element_4 b_D (io_tptp.powerset_3 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22)))) (= (io_tptp.in_5 b_D b_C) (io_tptp.in_5 (io_tptp.set_difference_7 (io_tptp.cast_as_carrier_subset_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) b_D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))))))))) (let ((_let_33 (not _let_32))) (let ((_let_34 (io_tptp.element_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_28))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.top_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.topological_space SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_35 _let_33))) (let ((_let_41 (forall ((A $$unsorted) (b_B it_3_$$unsorted)) (or (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (io_tptp.element_4 b_B (io_tptp.powerset_3 (io_tptp.powerset_3 (io_tptp.the_carrier_2 A))))) (not (forall ((b_C it_3_$$unsorted)) (or (not (io_tptp.element_4 b_C (io_tptp.powerset_3 (io_tptp.powerset_3 (io_tptp.the_carrier_2 A))))) (not (forall ((b_D it_3_$$unsorted)) (or (not (io_tptp.element_4 b_D (io_tptp.powerset_3 (io_tptp.the_carrier_2 A)))) (= (io_tptp.in_5 b_D b_C) (io_tptp.in_5 (io_tptp.set_difference_7 (io_tptp.cast_as_carrier_subset_6 A) b_D) b_B)))))))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (not _let_41))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (not (forall ((C $$unsorted)) (or (not (tptp.element C (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (not (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.powerset (tptp.the_carrier A)))) (= (tptp.in D C) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B))))))))))) _let_43))))))) (let ((_let_45 (or))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_44) :args (_let_43))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_41))) (REFL :args (_let_42)) :args _let_45)) _let_44 :args (_let_42 true _let_41)))) (let ((_let_47 (REFL :args (_let_40)))) (let ((_let_48 (_let_32))) (let ((_let_49 (forall ((b_C it_3_$$unsorted)) (or (not (io_tptp.in_5 b_C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71)) (io_tptp.in_5 b_C (io_tptp.powerset_3 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_29))) (let ((_let_52 (forall ((b_A it_3_$$unsorted) (b_B it_3_$$unsorted)) (or (not (forall ((b_C it_3_$$unsorted)) (or (not (io_tptp.in_5 b_C b_A)) (io_tptp.in_5 b_C b_B)))) (io_tptp.element_4 b_A (io_tptp.powerset_3 b_B)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B)))) (tptp.element A (tptp.powerset B)))) _let_52))))))) (let ((_let_54 (io_tptp.in_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_156 _let_7))) (let ((_let_55 (io_tptp.in_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_156 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54))) (let ((_let_58 (and _let_54 (io_tptp.in_5 (io_tptp.set_difference_7 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_156) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)))) (let ((_let_59 (= _let_55 _let_58))) (let ((_let_60 (forall ((b_D it_3_$$unsorted)) (= (and (io_tptp.in_5 b_D (io_tptp.powerset_3 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (io_tptp.in_5 (io_tptp.set_difference_7 (io_tptp.cast_as_carrier_subset_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) b_D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)) (io_tptp.in_5 b_D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71))))) (let ((_let_61 (forall ((b_C it_3_$$unsorted)) (not (forall ((b_D it_3_$$unsorted)) (= (io_tptp.in_5 b_D b_C) (and (io_tptp.in_5 b_D (io_tptp.powerset_3 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (io_tptp.in_5 (io_tptp.set_difference_7 (io_tptp.cast_as_carrier_subset_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) b_D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)))))))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_39 _let_37 _let_35 _let_62))) (let ((_let_64 (forall ((A $$unsorted) (b_B it_3_$$unsorted)) (or (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (io_tptp.element_4 b_B (io_tptp.powerset_3 (io_tptp.powerset_3 (io_tptp.the_carrier_2 A))))) (not (forall ((b_C it_3_$$unsorted)) (not (forall ((b_D it_3_$$unsorted)) (= (io_tptp.in_5 b_D b_C) (and (io_tptp.in_5 b_D (io_tptp.powerset_3 (io_tptp.the_carrier_2 A))) (io_tptp.in_5 (io_tptp.set_difference_7 (io_tptp.cast_as_carrier_subset_6 A) b_D) b_B))))))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.powerset (tptp.the_carrier A))) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B))))))))) _let_64))))))) (let ((_let_66 (_let_60))) (let ((_let_67 (_let_62))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_67)) :args _let_67) (REWRITE :args ((=> _let_62 (not (not (forall ((b_D it_3_$$unsorted)) (= (io_tptp.in_5 b_D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71) (and (io_tptp.in_5 b_D (io_tptp.powerset_3 (io_tptp.the_carrier_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (io_tptp.in_5 (io_tptp.set_difference_7 (io_tptp.cast_as_carrier_subset_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) b_D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) (REFL :args _let_66) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_39 _let_37 _let_35 _let_62 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_45)) :args ((or _let_38 _let_40))) _let_46 :args (_let_38 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_45)) :args ((or _let_36 _let_40))) _let_46 :args (_let_36 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 2)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_45)) :args ((or _let_34 _let_40))) _let_46 :args (_let_34 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING ((not (= (io_tptp.element_4 b_B (io_tptp.powerset_3 (io_tptp.powerset_3 (io_tptp.the_carrier_2 A)))) false))))) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_62 false _let_38 false _let_36 false _let_34 false _let_63)) :args (_let_60 true _let_61)))) (let ((_let_69 (ASSUME :args _let_66))) (let ((_let_70 (_let_50))) (let ((_let_71 (_let_27))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_71)) :args _let_71)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_25))) (REFL :args (_let_26)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_27 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_29 _let_50 (not _let_51)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_70)) :args _let_70)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) (REFL :args ((not _let_57))) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 0)) :args ((or _let_54 (not _let_58)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_59)) :args ((or _let_56 _let_58 (not _let_59)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_156 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_66))) _let_68 :args (_let_59 false _let_60)) (CNF_OR_NEG :args (_let_57 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 0)) (CONG (REFL :args (_let_57)) (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_45)) :args ((or _let_55 _let_57))) :args (_let_57 false _let_58 false _let_59 true _let_54 false _let_55)) :args (_let_49 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 _let_7 QUANTIFIERS_INST_E_MATCHING ((not (= (io_tptp.element_4 b_A (io_tptp.powerset_3 b_B)) true))))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_29 false _let_49 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (io_tptp.element_4 b_C _let_28) false))))) :args _let_48))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 3)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_45)) :args ((or _let_32 _let_40))) _let_46 :args (_let_32 true _let_40)) :args (_let_31 false _let_32)) :args (_let_27 false _let_29 false _let_31)) :args (_let_26 true _let_25)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 1)) _let_72 :args ((not _let_20) true _let_24)))) (let ((_let_74 (_let_20))) (let ((_let_75 (not _let_21))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_150 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_66))) _let_68 :args (_let_22 false _let_60)))) (let ((_let_77 (not _let_22))) (let ((_let_78 (_let_22))) (let ((_let_79 (not _let_17))) (let ((_let_80 (forall ((b_BOUND_VARIABLE_1419 it_3_$$unsorted) (b_BOUND_VARIABLE_1421 it_3_$$unsorted)) (or (io_tptp.empty_13 b_BOUND_VARIABLE_1419) (= (io_tptp.element_4 b_BOUND_VARIABLE_1421 b_BOUND_VARIABLE_1419) (io_tptp.in_5 b_BOUND_VARIABLE_1421 b_BOUND_VARIABLE_1419)))))) (let ((_let_81 (_let_80))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_8 _let_11 (not _let_12)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_81) :args (_let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_150 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_81)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_1419 $$unsorted) (BOUND_VARIABLE_1421 $$unsorted)) (or (tptp.empty BOUND_VARIABLE_1419) (= (tptp.element BOUND_VARIABLE_1421 BOUND_VARIABLE_1419) (tptp.in BOUND_VARIABLE_1421 BOUND_VARIABLE_1419)))) (forall ((BOUND_VARIABLE_1430 $$unsorted) (BOUND_VARIABLE_1432 $$unsorted)) (or (not (tptp.empty BOUND_VARIABLE_1430)) (= (tptp.element BOUND_VARIABLE_1432 BOUND_VARIABLE_1430) (tptp.empty BOUND_VARIABLE_1432))))) (and _let_80 (forall ((b_BOUND_VARIABLE_1430 it_3_$$unsorted) (b_BOUND_VARIABLE_1432 it_3_$$unsorted)) (or (not (io_tptp.empty_13 b_BOUND_VARIABLE_1430)) (= (io_tptp.element_4 b_BOUND_VARIABLE_1432 b_BOUND_VARIABLE_1430) (io_tptp.empty_13 b_BOUND_VARIABLE_1432)))))))))) :args (0)) :args (_let_12 false _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or _let_23 _let_9 _let_15))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_10))) :args _let_45)) :args ((or _let_10 _let_24))) _let_72 :args (_let_10 true _let_24)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_78) :args ((or _let_19 _let_75 _let_77))) _let_76 (REORDERING (CNF_AND_NEG :args (_let_21)) :args ((or _let_79 _let_21 _let_18))) (CNF_EQUIV_NEG2 :args _let_74) _let_73 :args ((or _let_79 _let_18) false _let_22 false _let_21 true _let_19 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_78) :args ((or (not _let_19) _let_21 _let_77))) _let_76 (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_17 _let_75))) (REORDERING (CNF_EQUIV_NEG1 :args _let_74) :args ((or _let_17 _let_19 _let_20))) _let_73 :args (_let_17 false _let_22 true _let_21 false _let_19 true _let_20)) :args (_let_18 false _let_17)) :args (_let_15 false _let_10 true _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (_let_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_13))) _let_14 :args ((not _let_8) false _let_13)) :args (false false _let_12 true _let_11 true _let_8)) :args (_let_5 (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_membered A))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered A))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_membered A))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (tptp.v1_xcmplx_0 B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.natural B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.v1_membered B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v2_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v3_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v4_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v5_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1) (tptp.v5_membered _let_1))))) true (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) true (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (tptp.element (tptp.cast_as_carrier_subset A) (tptp.powerset (tptp.the_carrier A))))) true (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))) true true (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (tptp.closed_subset (tptp.cast_as_carrier_subset A) A))) _let_4 _let_3 _let_2 true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (tptp.empty tptp.empty_set) _let_1 (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 66.40/66.58 )
% 66.40/66.58 % SZS output end Proof for SEU311+1
% 66.40/66.59 % cvc5---1.0.5 exiting
% 66.40/66.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------