%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU157+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n001.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 16:29:39 EDT 2023

% Result   : Theorem 51.17s 51.41s
% Output   : Proof 51.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU157+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n001.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
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Wed Aug 23 14:38:24 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 51.17/51.41  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.qXeFOLnJTF/cvc5---1.0.5_9788.p...
% 51.17/51.41  ------- get file name : TPTP file name is SEU157+2
% 51.17/51.41  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9788.smt2...
% 51.17/51.41  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 51.17/51.41  --- Run --no-e-matching --full-saturate-quant at 5...
% 51.17/51.41  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 51.17/51.41  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 51.17/51.41  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 51.17/51.41  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 51.17/51.41  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 51.17/51.41  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 51.17/51.41  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.17/51.41  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 51.17/51.41  % SZS status Theorem for SEU157+2
% 51.17/51.41  % SZS output start Proof for SEU157+2
% 51.17/51.41  (
% 51.17/51.41  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))))) (let ((_let_3 (not _let_2))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))))) (let ((_let_5 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_6 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (and _let_6 _let_5))) (let ((_let_8 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.in _let_9 _let_8))) (let ((_let_11 (= _let_10 _let_7))) (let ((_let_12 (not _let_7))) (let ((_let_13 (forall ((E $$unsorted) (F $$unsorted)) (or (not (tptp.in E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.in F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= (tptp.ordered_pair E F) (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_14 (not _let_13))) (let ((_let_15 (= _let_10 _let_14))) (let ((_let_16 (forall ((D $$unsorted)) (= (tptp.in D (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((E $$unsorted) (F $$unsorted)) (or (not (tptp.in E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.in F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= D (tptp.ordered_pair E F)))))))))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (not (forall ((E $$unsorted) (F $$unsorted)) (or (not (tptp.in E A)) (not (tptp.in F B)) (not (= D (tptp.ordered_pair E F)))))))))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_16))) (let ((_let_20 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_19) :args (_let_9 QUANTIFIERS_INST_CBQI_PROP)) :args _let_19))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_8 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_17)))) _let_18 :args (_let_16 false _let_17)) :args (_let_15 false _let_16)))) (let ((_let_21 (not _let_5))) (let ((_let_22 (not _let_6))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (not _let_15))) (let ((_let_25 (_let_15))) (let ((_let_26 (not _let_11))) (let ((_let_27 (_let_3))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 (or))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args _let_27)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) (REFL :args (_let_26)) :args _let_29)) _let_28 :args (_let_26 true _let_2)))) (let ((_let_31 (_let_11))) (let ((_let_32 (_let_13))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_32))) (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 (not _let_23)))) (REORDERING (CNF_AND_POS :args (_let_7 1)) :args ((or _let_5 _let_12))) (REORDERING (CNF_AND_POS :args (_let_7 0)) :args ((or _let_6 _let_12))) (REORDERING (CNF_EQUIV_NEG1 :args _let_31) :args ((or _let_10 _let_7 _let_11))) _let_30 (REORDERING (CNF_EQUIV_POS1 :args _let_25) :args ((or (not _let_10) _let_14 _let_24))) _let_20 :args (_let_14 true _let_23 false _let_5 false _let_6 false _let_7 true _let_11 true _let_10 false _let_15)))) (let ((_let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))))) (let ((_let_35 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_36 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_38 (and _let_35 _let_37))) (let ((_let_39 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_40 (= _let_9 _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_38))) (let ((_let_43 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (= (tptp.ordered_pair A B) (tptp.ordered_pair C D))) (and (= A C) (= B D)))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (not _let_45))) (let ((_let_47 (not _let_36))) (let ((_let_48 (or _let_47 _let_46 _let_41))) (let ((_let_49 (not _let_48))) (let ((_let_50 (_let_14))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50) (REWRITE :args ((=> _let_14 (not (or _let_47 _let_46 (not (= _let_39 _let_9))))))))) (CONG _let_34 (REFL :args (_let_49)) :args _let_29)) _let_33 :args (_let_49 true _let_13)))) (let ((_let_52 (REFL :args (_let_48)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_38 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_29)) :args ((or _let_40 _let_48))) _let_51 :args (_let_40 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_38 false _let_40 false _let_42)))) (let ((_let_54 (not _let_38))) (let ((_let_55 (and _let_36 _let_35))) (let ((_let_56 (_let_36 _let_35))) (let ((_let_57 (ASSUME :args (_let_36)))) (let ((_let_58 (APPLY_UF tptp.in))) (let ((_let_59 (ASSUME :args (_let_35)))) (let ((_let_60 (and _let_45 _let_37))) (let ((_let_61 (_let_45 _let_37))) (let ((_let_62 (ASSUME :args (_let_45)))) (let ((_let_63 (ASSUME :args (_let_37)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_60)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_63) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_63)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args _let_58) (TRUE_INTRO _let_62))) :args _let_61)) :args _let_61)) :args (true _let_60)) :args ((or _let_5 _let_46 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_29)) :args ((or _let_45 _let_48))) _let_51 :args (_let_45 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 1)) :args ((or _let_37 _let_54))) _let_53 :args (_let_37 false _let_38)) :args (_let_5 false _let_45 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_55)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_59) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_59)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args _let_58) (TRUE_INTRO _let_57))) :args _let_56)) :args _let_56)) :args (true _let_55)) :args ((or _let_6 _let_47 (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_36))) :args _let_29)) :args ((or _let_36 _let_48))) _let_51 :args (_let_36 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 0)) :args ((or _let_35 _let_54))) _let_53 :args (_let_35 false _let_38)) :args (_let_6 false _let_36 false _let_35)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_31) _let_30 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_25) (CONG (REFL :args (_let_24)) (REFL :args (_let_10)) _let_34 :args _let_29)) :args ((or _let_10 _let_13 _let_24))) _let_33 _let_20 :args (_let_10 true _let_13 false _let_15)) :args (_let_12 true _let_11 false _let_10)) :args (false false _let_5 false _let_6 true _let_7)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))) (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) true true true true true true true true true true (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (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)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) _let_3 (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (tptp.in C A) (tptp.in C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.in C A) (tptp.in C B))) _let_1))))) (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (tptp.in C (tptp.set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 51.17/51.41  )
% 51.17/51.41  % SZS output end Proof for SEU157+2
% 51.17/51.41  % cvc5---1.0.5 exiting
% 51.17/51.42  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------