%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU131+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n025.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 16:29:26 EDT 2023

% Result   : Theorem 1.74s 1.92s
% Output   : Proof 1.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU131+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n025.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Wed Aug 23 13:50:50 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.23/0.51  %----Proving TF0_NAR, FOF, or CNF
% 1.74/1.92  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.2PrjrQVjI4/cvc5---1.0.5_392.p...
% 1.74/1.92  ------- get file name : TPTP file name is SEU131+2
% 1.74/1.92  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_392.smt2...
% 1.74/1.92  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.74/1.92  % SZS status Theorem for SEU131+2
% 1.74/1.92  % SZS output start Proof for SEU131+2
% 1.74/1.92  (
% 1.74/1.92  (let ((_let_1 (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))))))) (let ((_let_2 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)))) (let ((_let_3 (not (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))) (let ((_let_7 (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))))) (let ((_let_8 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.empty_set))) (let ((_let_9 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (and _let_11 _let_10))) (let ((_let_13 (= _let_8 _let_12))) (let ((_let_14 (not _let_8))) (let ((_let_15 (not _let_11))) (let ((_let_16 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_14))) (let ((_let_19 (forall ((BOUND_VARIABLE_1076 $$unsorted) (BOUND_VARIABLE_1078 $$unsorted) (BOUND_VARIABLE_1092 $$unsorted)) (or (not (tptp.disjoint BOUND_VARIABLE_1076 BOUND_VARIABLE_1078)) (not (tptp.in BOUND_VARIABLE_1092 BOUND_VARIABLE_1076)) (not (tptp.in BOUND_VARIABLE_1092 BOUND_VARIABLE_1078)))))) (let ((_let_20 (_let_19))) (let ((_let_21 (= tptp.empty_set (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set)))) (let ((_let_22 (= _let_16 _let_21))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= tptp.empty_set (tptp.set_intersection2 A B)))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (forall ((A $$unsorted)) (= tptp.empty_set (tptp.set_intersection2 A tptp.empty_set))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or _let_15 _let_9))) (let ((_let_28 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_31 (= _let_30 _let_28))) (let ((_let_32 (not _let_28))) (let ((_let_33 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_33))) _let_34 :args (_let_31 false _let_33)))) (let ((_let_36 (= tptp.empty_set (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_37 (= _let_30 _let_36))) (let ((_let_38 (forall ((D $$unsorted)) (= (tptp.in D tptp.empty_set) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_39 (= _let_36 _let_38))) (let ((_let_40 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_175 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_41 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_175 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_40))) (let ((_let_44 (not _let_40))) (let ((_let_45 (and _let_41 _let_44))) (let ((_let_46 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_175 tptp.empty_set))) (let ((_let_47 (= _let_46 _let_45))) (let ((_let_48 (not _let_30))) (let ((_let_49 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (= tptp.empty_set (tptp.set_difference A B)))))) (let ((_let_50 (not _let_37))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (_let_37))) (let ((_let_56 (not _let_31))) (let ((_let_57 (_let_31))) (let ((_let_58 (_let_5))) (let ((_let_59 (ASSUME :args _let_58))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.empty_set QUANTIFIERS_INST_ENUM)) :args _let_58)) _let_59 :args (_let_39 false _let_5)))) (let ((_let_61 (not _let_39))) (let ((_let_62 (not _let_38))) (let ((_let_63 (_let_39))) (let ((_let_64 (_let_28))) (let ((_let_65 (_let_62))) (let ((_let_66 (forall ((B $$unsorted)) (not (tptp.in B tptp.empty_set))))) (let ((_let_67 (forall ((A $$unsorted)) (= (forall ((B $$unsorted)) (not (tptp.in B A))) (= tptp.empty_set A))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (_let_66))) (let ((_let_70 (not _let_45))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_40 _let_42 (not _let_43)))) (REORDERING (CNF_AND_POS :args (_let_45 1)) :args ((or _let_44 _let_70))) (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_41 _let_70))) (REORDERING (CNF_EQUIV_NEG1 :args (_let_47)) :args ((or _let_46 _let_45 _let_47))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_69) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_175 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in B tptp.empty_set) false))))) :args _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.empty_set QUANTIFIERS_INST_ENUM)) :args (_let_67)))) _let_68 :args (_let_66 false _let_67)) :args ((not _let_46) false _let_66)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_38))) (REFL :args ((not _let_47))) :args _let_52)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_64) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_175 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_64)) (REORDERING (CNF_EQUIV_POS2 :args _let_63) :args ((or _let_36 _let_62 _let_61))) _let_60 (REORDERING (CNF_EQUIV_POS1 :args _let_57) :args ((or _let_48 _let_28 _let_56))) _let_35 (CNF_EQUIV_NEG2 :args _let_55) _let_54 :args (_let_48 true _let_40 false _let_41 false _let_45 true _let_46 true _let_47 false _let_43 true _let_38 false _let_39 false _let_28 false _let_31 true _let_36 true _let_37)))) (let ((_let_72 (_let_32))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_72)) :args _let_72)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_57) :args ((or _let_30 _let_32 _let_56))) _let_71 _let_35 :args (_let_32 true _let_30 false _let_31)) :args (_let_29 true _let_28)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_11))) :args _let_52)) :args ((or _let_11 _let_27))) _let_73 :args (_let_11 true _let_27)))) (let ((_let_75 (_let_12))) (let ((_let_76 (_let_38))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_13)) :args ((or _let_8 (not _let_12) (not _let_13)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D tptp.empty_set)))) :args _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_63) :args ((or (not _let_36) _let_38 _let_61))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_55) :args ((or _let_30 _let_36 _let_37))) _let_71 _let_54 :args (_let_36 true _let_30 true _let_37)) _let_60 :args (_let_38 false _let_36 false _let_39)) :args (_let_13 false _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_75) (CONG (REFL :args _let_75) (REFL :args (_let_15)) (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_52)) :args ((or _let_15 _let_9 _let_12))) _let_74 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 1)) _let_73 :args (_let_10 true _let_27)) :args (_let_12 false _let_11 true _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_15 _let_17 _let_14 (not _let_18)))) _let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_22)) :args ((or _let_16 (not _let_21) (not _let_22)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set))))) :args (_let_25))) _let_26 :args (_let_21 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_16 false _let_21 false _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_20) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.disjoint BOUND_VARIABLE_1076 BOUND_VARIABLE_1078) false)) (not (= (tptp.in BOUND_VARIABLE_1092 BOUND_VARIABLE_1076) false))))) :args _let_20)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_18 false _let_19)) :args (_let_14 false _let_11 false _let_16 false _let_18)) :args (false false _let_13 false _let_12 true _let_8)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in 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)))) _let_7 (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_6 (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)))))) _let_5 _let_4 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)) _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)) (=> (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 $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (forall ((A $$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))) _let_2 (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 $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) _let_1 (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (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)) (=> (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))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.75/1.93  )
% 1.75/1.93  % SZS output end Proof for SEU131+2
% 1.75/1.93  % cvc5---1.0.5 exiting
% 1.75/1.93  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------