TSTP Solution File: SEU141+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU141+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 16:29:30 EDT 2023
% Result : Theorem 0.20s 0.57s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU141+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n021.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 : Wed Aug 23 13:51:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.38n6OX6xvS/cvc5---1.0.5_25004.p...
% 0.20/0.57 ------- get file name : TPTP file name is SEU141+2
% 0.20/0.57 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25004.smt2...
% 0.20/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.57 % SZS status Theorem for SEU141+2
% 0.20/0.57 % SZS output start Proof for SEU141+2
% 0.20/0.57 (
% 0.20/0.57 (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)))) (let ((_let_5 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))) (let ((_let_8 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_8))) (let ((_let_10 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.set_union2 _let_8 _let_9)))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_8))) (let ((_let_14 (= tptp.empty_set _let_10))) (let ((_let_15 (= _let_8 (tptp.set_union2 _let_8 tptp.empty_set)))) (let ((_let_16 (_let_2))) (let ((_let_17 (ASSUME :args _let_16))) (let ((_let_18 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_16))) _let_17 :args (_let_11 false _let_2)))) (let ((_let_19 (tptp.subset _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_12))) (let ((_let_22 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= B (tptp.set_union2 A (tptp.set_difference B A))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (_let_4))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference A B)))) :args _let_24)) _let_25 :args (_let_19 false _let_4)))) (let ((_let_27 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_28 (= _let_27 _let_13))) (let ((_let_29 (not _let_13))) (let ((_let_30 (= _let_27 _let_14))) (let ((_let_31 (= tptp.empty_set (tptp.set_difference _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_32 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= A (tptp.set_difference A B)))))) (let ((_let_33 (not _let_28))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (or))) (let ((_let_36 (not _let_32))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_34) :args (_let_36))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_35)) _let_34 :args (_let_33 true _let_32)))) (let ((_let_38 (_let_28))) (let ((_let_39 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= tptp.empty_set (tptp.set_intersection2 A B)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.disjoint A B)))) :args (_let_39))) _let_40 :args (_let_30 false _let_39)))) (let ((_let_42 (not _let_30))) (let ((_let_43 (not _let_14))) (let ((_let_44 (_let_30))) (let ((_let_45 (= _let_19 _let_31))) (let ((_let_46 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (= tptp.empty_set (tptp.set_difference A B)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (not _let_11))) (let ((_let_49 (and _let_13 _let_31 _let_11))) (let ((_let_50 (ASSUME :args (_let_11)))) (let ((_let_51 (SYMM _let_50))) (let ((_let_52 (ASSUME :args (_let_13)))) (let ((_let_53 (SYMM _let_52))) (let ((_let_54 (ASSUME :args (_let_31)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_49)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_50 _let_52 _let_54) (SCOPE (TRANS (SYMM (SYMM _let_54)) (CONG _let_53 (SYMM _let_53) :args (APPLY_UF tptp.set_difference)) _let_51) :args (_let_11 _let_13 _let_31))) :args (_let_13 _let_31 _let_11))) :args (true _let_49)) :args ((or _let_29 _let_14 (not _let_31) _let_48))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_20 _let_31 (not _let_45)))) _let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_31 false _let_19 false _let_45)) _let_18 (REORDERING (CNF_EQUIV_POS2 :args _let_44) :args ((or _let_27 _let_43 _let_42))) _let_41 (REORDERING (CNF_EQUIV_NEG1 :args _let_38) :args ((or _let_27 _let_13 _let_28))) _let_37 :args (_let_27 false _let_31 false _let_11 true _let_14 false _let_30 false _let_13 true _let_28)))) (let ((_let_56 (forall ((A $$unsorted)) (= A (tptp.set_union2 A tptp.empty_set))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (not _let_15))) (let ((_let_59 (_let_58))) (let ((_let_60 (ASSUME :args (_let_15)))) (let ((_let_61 (ASSUME :args (_let_29)))) (let ((_let_62 (REFL :args (_let_8)))) (let ((_let_63 (ASSUME :args (_let_12)))) (let ((_let_64 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_63 _let_50 _let_64 _let_61) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (TRANS (CONG _let_62 (TRANS (SYMM (SYMM _let_64)) (SYMM _let_51)) :args (APPLY_UF tptp.set_union2)) (SYMM _let_63)) _let_62 :args (=)) (FALSE_INTRO _let_61)) :args ((= _let_15 false)))) :args (_let_12 _let_11 _let_14 _let_29))) _let_60) :args (_let_29 _let_14 _let_12 _let_11 _let_15)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_59))) (TRUE_INTRO _let_60))) :args (_let_58 _let_15)) :args ((not (and _let_29 _let_14 _let_12 _let_11 _let_15)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_13))) (REFL :args (_let_43)) (REFL :args ((not _let_12))) (REFL :args (_let_48)) (REFL :args _let_59) :args _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A tptp.empty_set)))) :args (_let_56))) _let_57 :args (_let_15 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_44) :args ((or (not _let_27) _let_14 _let_42))) _let_55 _let_41 :args (_let_14 false _let_27 false _let_30)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_38) _let_37 _let_55 :args (_let_29 true _let_28 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_12 (not _let_21)))) _let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset A B) false))))) :args (_let_22))) _let_23 :args (_let_21 false _let_22)) :args (_let_12 false _let_19 false _let_21)) _let_18 :args (false false _let_15 false _let_14 true _let_13 false _let_12 false _let_11)) :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.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 $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (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)))))) (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 $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) _let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) true true true true (tptp.empty tptp.empty_set) (forall ((A $$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 $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) _let_6 (exists ((A $$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 $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$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)))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (forall ((A $$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_4 (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))) _let_3 _let_2 (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 $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))) _let_1 (forall ((A $$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))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.57 )
% 0.20/0.57 % SZS output end Proof for SEU141+2
% 0.20/0.57 % cvc5---1.0.5 exiting
% 0.20/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------