%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET162+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 14:38:00 EDT 2023

% Result   : Theorem 0.21s 0.54s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET162+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n014.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 16:28:17 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.HwDjxS5CXH/cvc5---1.0.5_25141.p...
% 0.21/0.54  ------- get file name : TPTP file name is SET162+4
% 0.21/0.54  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25141.smt2...
% 0.21/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.54  % SZS status Theorem for SET162+4
% 0.21/0.54  % SZS output start Proof for SET162+4
% 0.21/0.54  (
% 0.21/0.54  (let ((_let_1 (forall ((A $$unsorted)) (tptp.equal_set (tptp.union A tptp.empty_set) A)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (or _let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.empty_set)))) (let ((_let_9 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_9))) (let ((_let_11 (= _let_10 _let_8))) (let ((_let_12 (_let_4))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 ((tptp.member X (tptp.union A B))))) (let ((_let_15 (not _let_7))) (let ((_let_16 (or _let_15 _let_10))) (let ((_let_17 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set)))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_20 (= _let_19 _let_17))) (let ((_let_21 (not _let_17))) (let ((_let_22 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (_let_22))) (let ((_let_25 ((tptp.subset A B)))) (let ((_let_26 (tptp.subset _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (and _let_26 _let_19))) (let ((_let_28 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_29 (= _let_26 _let_28))) (let ((_let_30 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_9))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.empty_set))) (let ((_let_35 (or _let_30 _let_34))) (let ((_let_36 (= _let_31 _let_35))) (let ((_let_37 (or))) (let ((_let_38 (_let_3))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (not _let_28))) (let ((_let_41 (_let_40))) (let ((_let_42 (tptp.equal_set _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (= _let_42 _let_27))) (let ((_let_44 (not _let_27))) (let ((_let_45 (_let_5))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (not _let_42))) (let ((_let_48 (_let_2))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (_let_21))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_17))) (REFL :args (_let_18)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_20)) :args ((or _let_19 _let_21 (not _let_20)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_43)) :args ((or _let_42 _let_44 (not _let_43)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_47)) :args _let_37)) _let_49 :args (_let_47 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_45)) _let_46 :args (_let_43 false _let_5)) :args (_let_44 true _let_42 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_29)) :args ((or _let_26 _let_40 (not _let_29)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_41)) :args _let_41)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_28))) (REFL :args ((not _let_33))) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_30 _let_34 (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X tptp.empty_set) false))))) :args _let_38)) _let_39 :args ((not _let_34) false _let_3)) (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or _let_32 _let_35 (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_36 false _let_4)) (CNF_OR_NEG :args (_let_33 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_37)) :args ((or _let_31 _let_33))) :args (_let_33 true _let_34 false _let_35 false _let_36 true _let_30 false _let_31)) :args (_let_28 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_29 false _let_22)) :args (_let_26 false _let_28 false _let_29)) :args ((not _let_19) true _let_27 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_20 false _let_22)) :args (_let_21 true _let_19 false _let_20)) :args (_let_18 true _let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_11)) :args ((or _let_10 (not _let_8) (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_8 0)) :args ((or _let_15 _let_8))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG (REFL :args (_let_16)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_7))) :args _let_37)) :args ((or _let_7 _let_16))) _let_51 :args (_let_7 true _let_16)) :args (_let_8 false _let_7)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_16 1)) _let_51 :args ((not _let_10) true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.empty_set QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_11 false _let_4)) :args (false false _let_8 true _let_10 false _let_11)) :args (_let_6 _let_5 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) _let_4 _let_3 (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55  )
% 0.21/0.55  % SZS output end Proof for SET162+4
% 0.21/0.55  % cvc5---1.0.5 exiting
% 0.21/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------