TSTP Solution File: SEU106+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 16:29:17 EDT 2023
% Result : Theorem 0.20s 0.69s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n029.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 01:23:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.69 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.iYo4c3yPcg/cvc5---1.0.5_6712.p...
% 0.20/0.69 ------- get file name : TPTP file name is SEU106+1
% 0.20/0.69 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6712.smt2...
% 0.20/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.69 % SZS status Theorem for SEU106+1
% 0.20/0.69 % SZS output start Proof for SEU106+1
% 0.20/0.69 (
% 0.20/0.69 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.symmetric_difference (tptp.symmetric_difference A B) (tptp.set_union2 A B)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))) (let ((_let_3 (not (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (=> (forall ((B $$unsorted)) (=> (tptp.element B A) (forall ((C $$unsorted)) (=> (tptp.element C A) (and (tptp.in (tptp.symmetric_difference B C) A) (tptp.in (tptp.set_union2 B C) A)))))) (tptp.preboolean A))))))) (let ((_let_4 (forall ((A $$unsorted)) (= (tptp.preboolean A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in B A) (tptp.in C A)) (and (tptp.in (tptp.set_union2 B C) A) (tptp.in (tptp.set_difference B C) A)))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A B) (tptp.symmetric_difference A (tptp.set_intersection2 A B)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.symmetric_difference A B) (tptp.set_union2 (tptp.set_difference A B) (tptp.set_difference B A)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.symmetric_difference A B) (tptp.symmetric_difference B A))))) (let ((_let_8 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_9 (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_10 (tptp.symmetric_difference _let_9 _let_8))) (let ((_let_11 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (tptp.symmetric_difference _let_8 _let_9))) (let ((_let_14 (= _let_10 _let_13))) (let ((_let_15 (= _let_10 (tptp.set_union2 (tptp.set_difference _let_9 _let_8) (tptp.set_difference _let_8 _let_9))))) (let ((_let_16 (tptp.in _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (tptp.in _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_18 (_let_1))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 (_let_7))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (_let_6))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 (tptp.element _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_25 (not _let_16))) (let ((_let_26 (or _let_25 _let_24))) (let ((_let_27 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.element A B))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_27))) (let ((_let_30 (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_11))) (let ((_let_31 (tptp.in _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_32 (and _let_31 (tptp.in (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_33 (not _let_24))) (let ((_let_34 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_32))) (let ((_let_37 (forall ((B $$unsorted) (BOUND_VARIABLE_1216 $$unsorted)) (or (not (tptp.element B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.element BOUND_VARIABLE_1216 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (and (tptp.in (tptp.symmetric_difference B BOUND_VARIABLE_1216) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in (tptp.set_union2 B BOUND_VARIABLE_1216) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_38 (tptp.preboolean SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_39 (not _let_37))) (let ((_let_40 (or (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_39 _let_38))) (let ((_let_41 (forall ((A $$unsorted)) (or (tptp.empty A) (not (forall ((B $$unsorted) (BOUND_VARIABLE_1216 $$unsorted)) (or (not (tptp.element B A)) (not (tptp.element BOUND_VARIABLE_1216 A)) (and (tptp.in (tptp.symmetric_difference B BOUND_VARIABLE_1216) A) (tptp.in (tptp.set_union2 B BOUND_VARIABLE_1216) A))))) (tptp.preboolean A))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_43) :args (_let_45))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) _let_43 :args (_let_42 true _let_41)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_37))) :args _let_44)) :args ((or _let_37 _let_40))) _let_46 :args (_let_37 true _let_40)))) (let ((_let_48 (_let_37))) (let ((_let_49 ((tptp.symmetric_difference B BOUND_VARIABLE_1216)))) (let ((_let_50 (ASSUME :args _let_48))) (let ((_let_51 (not _let_32))) (let ((_let_52 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_53 (= _let_52 _let_30))) (let ((_let_54 (tptp.in _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_55 (not _let_31))) (let ((_let_56 (_let_5))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (tptp.in _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_59 (and _let_58 _let_54))) (let ((_let_60 (not _let_54))) (let ((_let_61 (tptp.in _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_62 (and _let_61 _let_58))) (let ((_let_63 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_35 _let_64 _let_62))) (let ((_let_66 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_63))) (let ((_let_69 ((not (= (tptp.in A B) false))))) (let ((_let_70 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_67 _let_59))) (let ((_let_73 (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (and (tptp.in (tptp.set_union2 B C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in (tptp.set_difference B C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_74 (not _let_72))) (let ((_let_75 (= _let_38 _let_73))) (let ((_let_76 (not _let_73))) (let ((_let_77 (forall ((A $$unsorted)) (= (tptp.preboolean A) (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B A)) (not (tptp.in C A)) (and (tptp.in (tptp.set_union2 B C) A) (tptp.in (tptp.set_difference B C) A)))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (_let_76))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_73))) (REFL :args (_let_74)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_75)) :args ((or _let_38 _let_76 (not _let_75)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 2)) _let_46 :args ((not _let_38) true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.preboolean A)))) :args (_let_77))) _let_78 :args (_let_75 false _let_77)) :args (_let_76 true _let_38 false _let_75)) :args (_let_74 true _let_73)))) (let ((_let_81 (REFL :args (_let_72)))) (let ((_let_82 (or _let_71 _let_34))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_71 _let_34 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_44)) :args ((or _let_70 _let_72))) _let_80 :args (_let_70 true _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_29)) _let_28 :args (_let_82 false _let_27)) :args (_let_34 false _let_70 false _let_82)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_35 _let_64 _let_62 (not _let_65)))) _let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_63 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 1)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_44)) :args ((or _let_66 _let_72))) _let_80 :args (_let_66 true _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_29)) _let_28 :args (_let_68 false _let_27)) :args (_let_63 false _let_66 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 B BOUND_VARIABLE_1216)))) :args _let_48)) _let_47 :args (_let_65 false _let_37)) :args (_let_62 false _let_34 false _let_63 false _let_65)))) (let ((_let_85 (not _let_62))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_62 1)) :args ((or _let_58 _let_85))) _let_84 :args (_let_58 false _let_62)))) (let ((_let_87 (and _let_60 _let_53))) (let ((_let_88 (_let_60 _let_53))) (let ((_let_89 (ASSUME :args (_let_60)))) (let ((_let_90 (APPLY_UF tptp.in))) (let ((_let_91 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_92 (ASSUME :args (_let_53)))) (let ((_let_93 (and _let_17 (tptp.in (tptp.set_union2 _let_8 _let_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_94 (tptp.element _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_95 (not _let_94))) (let ((_let_96 (tptp.element _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_95 _let_93))) (let ((_let_99 (not _let_61))) (let ((_let_100 (or _let_99 _let_94))) (let ((_let_101 (not _let_58))) (let ((_let_102 (or _let_101 _let_96))) (let ((_let_103 (and _let_12 _let_14 _let_15 _let_25))) (let ((_let_104 (ASSUME :args (_let_25)))) (let ((_let_105 (ASSUME :args (_let_12)))) (let ((_let_106 (ASSUME :args (_let_15)))) (let ((_let_107 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_103)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_104 _let_105 _let_106 _let_107) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (SYMM _let_107) _let_106) _let_91 :args _let_90) (CONG (TRANS (SYMM _let_106) (SYMM _let_105)) _let_91 :args _let_90) (FALSE_INTRO _let_104))) :args (_let_25 _let_12 _let_15 _let_14))) :args (_let_12 _let_14 _let_15 _let_25))) :args (true _let_103)) (CONG (REFL :args ((not _let_12))) (REFL :args ((not _let_14))) (REFL :args ((not _let_15))) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_16))) (REFL :args ((not _let_17))) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 0)) :args ((or _let_17 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_97 _let_95 _let_93 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_101 _let_96 (not _let_102)))) _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_29)) _let_28 :args (_let_102 false _let_27)) :args (_let_96 false _let_58 false _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_99 _let_94 (not _let_100)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_62 0)) :args ((or _let_61 _let_85))) _let_84 :args (_let_61 false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_29)) _let_28 :args (_let_100 false _let_27)) :args (_let_94 false _let_61 false _let_100)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_8 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_98 false _let_37)) :args (_let_93 false _let_96 false _let_94 false _let_98)) :args (_let_17 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_24 _let_25 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_33 _let_32 (not _let_36)))) _let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 0)) :args ((or _let_31 _let_51))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_89 _let_92) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_92) _let_91 :args _let_90) (FALSE_INTRO _let_89))) :args _let_88)) :args _let_88)) :args (true _let_87)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_54))) (REFL :args ((not _let_53))) (REFL :args (_let_55)) :args _let_44)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_59)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_72 2)) _let_80 :args ((not _let_59) true _let_72)) _let_86 :args (_let_60 true _let_59 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference A B)))) :args _let_56)) _let_57 :args (_let_53 false _let_5)) :args (_let_55 true _let_54 false _let_53)) :args (_let_51 true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_36 false _let_37)) :args (_let_33 false _let_34 true _let_32 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.element A B) true))))) :args _let_29)) _let_28 :args (_let_26 false _let_27)) :args (_let_25 true _let_24 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_9 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.symmetric_difference A B)))) :args _let_22)) _let_23 :args (_let_15 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_9 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.symmetric_difference A B)))) :args _let_20)) _let_21 :args (_let_14 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_18)) _let_19 :args (_let_12 false _let_1)) :args (false false _let_17 true _let_16 false _let_15 false _let_14 false _let_12)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.preboolean A) (and (tptp.cup_closed A) (tptp.diff_closed A)))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (and (tptp.cup_closed A) (tptp.diff_closed A)) (tptp.preboolean A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) _let_7 _let_6 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite B) (tptp.finite (tptp.set_intersection2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_intersection2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.symmetric_difference A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.set_union2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.cup_closed A) (tptp.cap_closed A) (tptp.diff_closed A) (tptp.preboolean A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B) (tptp.natural B) (tptp.finite B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_5 _let_4 _let_3 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_2 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (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)) (= (tptp.symmetric_difference A tptp.empty_set) A)) (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.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)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.69 )
% 0.20/0.69 % SZS output end Proof for SEU106+1
% 0.20/0.69 % cvc5---1.0.5 exiting
% 0.20/0.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------