%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU102+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n022.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 1.52s 1.72s
% Output   : Proof 1.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SEU102+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 12:16:11 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 1.52/1.72  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.i9HHGMxIok/cvc5---1.0.5_19289.p...
% 1.52/1.72  ------- get file name : TPTP file name is SEU102+1
% 1.52/1.72  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19289.smt2...
% 1.52/1.72  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.52/1.72  % SZS status Theorem for SEU102+1
% 1.52/1.72  % SZS output start Proof for SEU102+1
% 1.52/1.72  (
% 1.52/1.72  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.preboolean C)) (=> (and (tptp.element A C) (tptp.element B C)) (tptp.element (tptp.set_intersection2 A B) C))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.preboolean A) (tptp.element B A) (tptp.element C A)) (= (tptp.prebool_difference A B C) (tptp.set_difference B C)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.preboolean A) (tptp.element B A) (tptp.element C A)) (tptp.element (tptp.prebool_difference A B C) A))))) (let ((_let_5 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_6 (tptp.element _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_7 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7))) (let ((_let_9 (= _let_5 _let_8))) (let ((_let_10 (tptp.prebool_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7))) (let ((_let_11 (= _let_8 _let_10))) (let ((_let_12 (tptp.element _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_13 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.preboolean SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_20 (or _let_19 _let_18 _let_16 _let_14 _let_6))) (let ((_let_21 (not _let_6))) (let ((_let_22 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty C) (not (tptp.preboolean C)) (not (tptp.element A C)) (not (tptp.element B C)) (tptp.element (tptp.set_intersection2 A B) C))))) (let ((_let_23 (not _let_20))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (or))) (let ((_let_26 (not _let_22))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_24) :args (_let_26))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_22))) (REFL :args (_let_23)) :args _let_25)) _let_24 :args (_let_23 true _let_22)))) (let ((_let_28 (_let_1))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 (tptp.element _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_19 _let_18 _let_16 _let_31 _let_11))) (let ((_let_33 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty A) (not (tptp.preboolean A)) (not (tptp.element B A)) (not (tptp.element C A)) (= (tptp.prebool_difference A B C) (tptp.set_difference B C)))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 ((tptp.set_difference B C) (not (= (tptp.element B A) false))))) (let ((_let_37 (tptp.prebool_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_38 (tptp.element _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_39 (= _let_7 _let_37))) (let ((_let_40 (or _let_19 _let_18 _let_16 _let_14 _let_38))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty A) (not (tptp.preboolean A)) (not (tptp.element B A)) (not (tptp.element C A)) (tptp.element (tptp.prebool_difference A B C) A))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((tptp.prebool_difference A B C)))) (let ((_let_45 (REFL :args (_let_20)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 3)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_25)) :args ((or _let_13 _let_20))) _let_27 :args (_let_13 true _let_20)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 2)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_25)) :args ((or _let_15 _let_20))) _let_27 :args (_let_15 true _let_20)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_25)) :args ((or _let_17 _let_20))) _let_27 :args (_let_17 true _let_20)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 0)) _let_27 :args ((not _let_19) true _let_20)))) (let ((_let_50 (or _let_19 _let_18 _let_16 _let_14 _let_39))) (let ((_let_51 (and _let_39 _let_38))) (let ((_let_52 (ASSUME :args (_let_38)))) (let ((_let_53 (APPLY_UF tptp.element))) (let ((_let_54 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_55 (ASSUME :args (_let_39)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_51)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_52 _let_55) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_55)) _let_54 :args _let_53) (TRUE_INTRO _let_52))) :args (_let_38 _let_39))) :args (_let_39 _let_38))) :args (true _let_51)) :args ((or (not _let_39) _let_30 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_39 (not _let_50)))) _let_49 _let_48 _let_47 _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING _let_36)) :args _let_35))) _let_34 :args (_let_50 false _let_33)) :args (_let_39 true _let_19 false _let_17 false _let_15 false _let_13 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_38 (not _let_40)))) _let_49 _let_48 _let_47 _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_40 false _let_41)) :args (_let_38 true _let_19 false _let_17 false _let_15 false _let_13 false _let_40)) :args (_let_30 false _let_39 false _let_38)))) (let ((_let_57 (or _let_19 _let_18 _let_16 _let_31 _let_12))) (let ((_let_58 (ASSUME :args (_let_12)))) (let ((_let_59 (ASSUME :args (_let_11)))) (let ((_let_60 (ASSUME :args (_let_9)))) (let ((_let_61 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_58 _let_59 _let_60 _let_61) :args (_let_21 _let_9 _let_11 _let_12)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_61)) (CONG (TRANS (SYMM (SYMM _let_60)) (SYMM (SYMM _let_59))) _let_54 :args _let_53) (TRUE_INTRO _let_58))) :args (_let_12 _let_11 _let_9 _let_21)) :args ((not (and _let_21 _let_9 _let_11 _let_12)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_6))) (REFL :args ((not _let_9))) (REFL :args ((not _let_11))) (REFL :args ((not _let_12))) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_19 _let_18 _let_16 _let_31 _let_12 (not _let_57)))) _let_49 _let_48 _let_47 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_57 false _let_41)) :args (_let_12 true _let_19 false _let_17 false _let_15 false _let_30 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_19 _let_18 _let_16 _let_31 _let_11 (not _let_32)))) _let_49 _let_48 _let_47 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7 QUANTIFIERS_INST_E_MATCHING _let_36)) :args _let_35))) _let_34 :args (_let_32 false _let_33)) :args (_let_11 true _let_19 false _let_17 false _let_15 false _let_30 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_28))) _let_29 :args (_let_9 false _let_1)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 4)) _let_27 :args (_let_21 true _let_20)) :args (false false _let_12 false _let_11 false _let_9 true _let_6)) :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 $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) _let_4 (forall ((A $$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)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (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))))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (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))) _let_1 (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 $$unsorted) (B $$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)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.52/1.73  )
% 1.52/1.73  % SZS output end Proof for SEU102+1
% 1.52/1.73  % cvc5---1.0.5 exiting
% 1.52/1.73  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------