TSTP Solution File: SEU104+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 16:29:16 EDT 2023
% Result : Theorem 0.16s 0.63s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11 % Command : do_cvc5 %s %d
% 0.10/0.31 % Computer : n024.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 23 15:32:54 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.42 %----Proving TF0_NAR, FOF, or CNF
% 0.16/0.63 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.QybqL2eaeW/cvc5---1.0.5_23248.p...
% 0.16/0.63 ------- get file name : TPTP file name is SEU104+1
% 0.16/0.63 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23248.smt2...
% 0.16/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.16/0.63 % SZS status Theorem for SEU104+1
% 0.16/0.63 % SZS output start Proof for SEU104+1
% 0.16/0.63 (
% 0.16/0.63 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.symmetric_difference A (tptp.set_difference B A)))))) (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 $$unsorted)) (=> (tptp.element C A) (and (tptp.in (tptp.symmetric_difference B C) A) (tptp.in (tptp.set_difference B C) A)))))) (tptp.preboolean A))))))) (let ((_let_4 (forall ((A $$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)) (or (not (tptp.in A B)) (tptp.element A B))))) (let ((_let_6 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_7 (tptp.element _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (tptp.in _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_12 (not _let_10))) (let ((_let_13 (and (tptp.in (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_8))) (let ((_let_14 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_13))) (let ((_let_19 (forall ((B $$unsorted) (BOUND_VARIABLE_1159 $$unsorted)) (or (not (tptp.element B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.element BOUND_VARIABLE_1159 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (and (tptp.in (tptp.symmetric_difference B BOUND_VARIABLE_1159) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in (tptp.set_difference B BOUND_VARIABLE_1159) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_20 (tptp.preboolean SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (not _let_19))) (let ((_let_22 (or (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_21 _let_20))) (let ((_let_23 (forall ((A $$unsorted)) (or (tptp.empty A) (not (forall ((B $$unsorted) (BOUND_VARIABLE_1159 $$unsorted)) (or (not (tptp.element B A)) (not (tptp.element BOUND_VARIABLE_1159 A)) (and (tptp.in (tptp.symmetric_difference B BOUND_VARIABLE_1159) A) (tptp.in (tptp.set_difference B BOUND_VARIABLE_1159) A))))) (tptp.preboolean A))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (or))) (let ((_let_27 (not _let_23))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_27))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) _let_25 :args (_let_24 true _let_23)))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_19))) :args _let_26)) :args ((or _let_19 _let_22))) _let_28 :args (_let_19 true _let_22)))) (let ((_let_30 (_let_19))) (let ((_let_31 ((tptp.symmetric_difference B BOUND_VARIABLE_1159)))) (let ((_let_32 (ASSUME :args _let_30))) (let ((_let_33 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_16))) (let ((_let_36 (_let_5))) (let ((_let_37 ((not (= (tptp.in A B) false))))) (let ((_let_38 (tptp.in (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_39 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_40 (tptp.in _let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_41 (and _let_40 _let_38))) (let ((_let_42 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_34 _let_41))) (let ((_let_45 (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (and (tptp.in (tptp.set_union2 B C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in (tptp.set_difference B C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_46 (not _let_44))) (let ((_let_47 (= _let_20 _let_45))) (let ((_let_48 (not _let_45))) (let ((_let_49 (forall ((A $$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_50 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_48))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_51)) :args _let_51)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_45))) (REFL :args (_let_46)) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_47)) :args ((or _let_20 _let_48 (not _let_47)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 2)) _let_28 :args ((not _let_20) true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.preboolean A)))) :args (_let_49))) _let_50 :args (_let_47 false _let_49)) :args (_let_48 true _let_20 false _let_47)) :args (_let_46 true _let_45)))) (let ((_let_53 (REFL :args (_let_44)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_16 (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 1)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_26)) :args ((or _let_33 _let_44))) _let_52 :args (_let_33 true _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_11 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_11 :args (_let_35 false _let_5)) :args (_let_16 false _let_33 false _let_35)))) (let ((_let_55 (or _let_43 _let_14))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_43 _let_14 (not _let_55)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 0)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_26)) :args ((or _let_42 _let_44))) _let_52 :args (_let_42 true _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_11 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_11 :args (_let_55 false _let_5)) :args (_let_14 false _let_42 false _let_55)))) (let ((_let_57 (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_6))) (let ((_let_58 (tptp.in _let_57 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_59 (and _let_58 (tptp.in (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_60 (not _let_7))) (let ((_let_61 (or _let_15 _let_60 _let_59))) (let ((_let_62 (not _let_59))) (let ((_let_63 (= _let_39 _let_57))) (let ((_let_64 (not _let_58))) (let ((_let_65 (_let_1))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (not _let_40))) (let ((_let_68 (and (tptp.in (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_38))) (let ((_let_69 (or _let_15 _let_17 _let_68))) (let ((_let_70 (and _let_67 _let_63))) (let ((_let_71 (_let_67 _let_63))) (let ((_let_72 (ASSUME :args (_let_67)))) (let ((_let_73 (ASSUME :args (_let_63)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_11 :args (_let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_7 _let_9 _let_12))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_15 _let_60 _let_59 (not _let_61)))) _let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 0)) :args ((or _let_58 _let_62))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_70)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_73) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_73) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args (APPLY_UF tptp.in)) (FALSE_INTRO _let_72))) :args _let_71)) :args _let_71)) :args (true _let_70)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_40))) (REFL :args ((not _let_63))) (REFL :args (_let_64)) :args _let_26)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_41)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_44 2)) _let_52 :args ((not _let_41) true _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 1)) :args ((or _let_38 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_15 _let_17 _let_68 (not _let_69)))) _let_56 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference B BOUND_VARIABLE_1159)))) :args _let_30)) _let_29 :args (_let_69 false _let_19)) :args (_let_68 false _let_14 false _let_16 false _let_69)) :args (_let_38 false _let_68)) :args (_let_67 true _let_41 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_65)) _let_66 :args (_let_63 false _let_1)) :args (_let_64 true _let_40 false _let_63)) :args (_let_62 true _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_30)) _let_29 :args (_let_61 false _let_19)) :args (_let_60 false _let_14 true _let_59 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 1)) :args ((or _let_8 (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_15 _let_17 _let_13 (not _let_18)))) _let_56 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_30)) _let_29 :args (_let_18 false _let_19)) :args (_let_13 false _let_14 false _let_16 false _let_18)) :args (_let_8 false _let_13)) :args (_let_12 true _let_7 false _let_8)) _let_11 :args (false true _let_10 false _let_5)) :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 $$unsorted)) (= (tptp.symmetric_difference A B) (tptp.symmetric_difference B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.symmetric_difference A B) (tptp.set_union2 (tptp.set_difference A B) (tptp.set_difference B A)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$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)) (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_4 _let_3 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_2 (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.16/0.64 )
% 0.16/0.64 % SZS output end Proof for SEU104+1
% 0.16/0.64 % cvc5---1.0.5 exiting
% 0.16/0.64 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------