TSTP Solution File: SET636^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET636^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 14:39:41 EDT 2023
% Result : Theorem 0.20s 0.79s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET636^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n019.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 : Sat Aug 26 11:53:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 0.20/0.79 %------------------------------------------------------------------------------
% 0.20/0.79 % File : SET636^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.79 % Domain : Set Theory
% 0.20/0.79 % Problem : TPS problem BOOL-PROP-118
% 0.20/0.79 % Version : Especial.
% 0.20/0.79 % English : Trybulec's 118th Boolean property of sets
% 0.20/0.79
% 0.20/0.79 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.79 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.79 % Source : [Bro09]
% 0.20/0.79 % Names : tps_0428 [Bro09]
% 0.20/0.79 % : BOOL-PROP-118 [TPS]
% 0.20/0.79
% 0.20/0.79 % Status : Theorem
% 0.20/0.79 % Rating : 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.20/0.79 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.20/0.79 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.20/0.79 % Maximal formula atoms : 1 ( 2 avg)
% 0.20/0.79 % Number of connectives : 8 ( 1 ~; 0 |; 2 &; 4 @)
% 0.20/0.79 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.79 % Maximal formula depth : 8 ( 8 avg)
% 0.20/0.79 % Number of types : 2 ( 1 usr)
% 0.20/0.79 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.79 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.20/0.79 % Number of variables : 5 ( 2 ^; 2 !; 1 ?; 5 :)
% 0.20/0.79 % SPC : TH0_THM_EQU_NAR
% 0.20/0.79
% 0.20/0.79 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.79 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.79 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.79 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.79 % : Polymorphic definitions expanded.
% 0.20/0.79 %------------------------------------------------------------------------------
% 0.20/0.79 thf(a_type,type,
% 0.20/0.79 a: $tType ).
% 0.20/0.79
% 0.20/0.79 thf(cBOOL_PROP_118_pme,conjecture,
% 0.20/0.79 ! [X: a > $o,Y: a > $o] :
% 0.20/0.79 ( ~ ? [Xx: a] :
% 0.20/0.79 ( ( X @ Xx )
% 0.20/0.79 & ( Y @ Xx ) )
% 0.20/0.79 <=> ( ( ^ [Xx: a] :
% 0.20/0.79 ( ( X @ Xx )
% 0.20/0.79 & ( Y @ Xx ) ) )
% 0.20/0.79 = ( ^ [Xx: a] : $false ) ) ) ).
% 0.20/0.79
% 0.20/0.79 %------------------------------------------------------------------------------
% 0.20/0.79 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3z6X4lh1QE/cvc5---1.0.5_5664.p...
% 0.20/0.79 (declare-sort $$unsorted 0)
% 0.20/0.79 (declare-sort tptp.a 0)
% 0.20/0.79 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (= (not (exists ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx)))) (= (lambda ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))) (lambda ((Xx tptp.a)) false))))))
% 0.20/0.79 (set-info :filename cvc5---1.0.5_5664)
% 0.20/0.79 (check-sat-assuming ( true ))
% 0.20/0.79 ------- get file name : TPTP file name is SET636^5
% 0.20/0.79 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5664.smt2...
% 0.20/0.79 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.79 % SZS status Theorem for SET636^5
% 0.20/0.79 % SZS output start Proof for SET636^5
% 0.20/0.79 (
% 0.20/0.79 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (= (not (exists ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx)))) (= (lambda ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))) (lambda ((Xx tptp.a)) false))))))) (let ((_let_2 (forall ((BOUND_VARIABLE_640 tptp.a)) (not (ho_4 k_8 BOUND_VARIABLE_640))))) (let ((_let_3 (ho_4 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_416))) (let ((_let_4 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_5 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_6 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_7 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_8 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_9 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_10 (forall ((BOUND_VARIABLE_670 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_667 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_647 tptp.a)) (= (ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_670) BOUND_VARIABLE_667) BOUND_VARIABLE_647) (and (ho_4 BOUND_VARIABLE_670 BOUND_VARIABLE_647) (ho_4 BOUND_VARIABLE_667 BOUND_VARIABLE_647)))))) (let ((_let_11 (forall ((BOUND_VARIABLE_694 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_693 |u_(-> tptp.a Bool)|)) (= (= k_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_694) BOUND_VARIABLE_693)) (forall ((Xx tptp.a)) (or (not (ho_4 BOUND_VARIABLE_694 Xx)) (not (ho_4 BOUND_VARIABLE_693 Xx)))))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (forall ((BOUND_VARIABLE_645 (-> tptp.a Bool)) (BOUND_VARIABLE_646 (-> tptp.a Bool)) (BOUND_VARIABLE_647 tptp.a)) (= (and (@ BOUND_VARIABLE_645 BOUND_VARIABLE_647) (@ BOUND_VARIABLE_646 BOUND_VARIABLE_647)) (ll_3 BOUND_VARIABLE_645 BOUND_VARIABLE_646 BOUND_VARIABLE_647))))) (let ((_let_14 (forall ((BOUND_VARIABLE_640 tptp.a)) (not (ll_2 BOUND_VARIABLE_640))))) (let ((_let_15 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (= (forall ((Xx tptp.a)) (or (not (@ X Xx)) (not (@ Y Xx)))) (= ll_2 (@ (@ ll_3 X) Y))))))) (let ((_let_16 (and _let_15 _let_14 _let_13))) (let ((_let_17 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (= (forall ((Xx tptp.a)) (or (not (@ X Xx)) (not (@ Y Xx)))) (= (lambda ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))) (lambda ((BOUND_VARIABLE_615 tptp.a)) false))))) _let_15))))) (PREPROCESS :args ((and _let_14 _let_13)))) :args (_let_16)) (PREPROCESS :args ((= _let_16 (and _let_12 _let_2 _let_10))))) (PREPROCESS :args ((and _let_9 _let_8 _let_7 _let_6 _let_5 _let_4)))) :args ((and _let_12 _let_2 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4))))) (let ((_let_18 (AND_ELIM _let_17 :args (1)))) (let ((_let_19 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_20 (ho_4 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_416))) (let ((_let_21 (= _let_20 _let_3))) (let ((_let_22 (forall ((z tptp.a)) (= (ho_4 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) z) (ho_4 k_8 z))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (= k_8 _let_19))) (let ((_let_25 (not _let_22))) (let ((_let_26 (or _let_25 _let_24))) (let ((_let_27 (_let_5))) (let ((_let_28 (forall ((Xx tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Xx)) (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx)))))) (let ((_let_29 (= _let_24 _let_28))) (let ((_let_30 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_31 (not _let_30))) (let ((_let_32 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31))) (let ((_let_35 (and _let_32 _let_30))) (let ((_let_36 (ho_4 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_37 (= _let_36 _let_35))) (let ((_let_38 (ho_4 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_39 (not _let_24))) (let ((_let_40 (not _let_29))) (let ((_let_41 (or))) (let ((_let_42 (_let_12))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_42)) :args _let_42)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) (REFL :args (_let_40)) :args _let_41)) (AND_ELIM _let_17 :args (0)) :args (_let_40 true _let_11)))) (let ((_let_44 (_let_29))) (let ((_let_45 (not _let_28))) (let ((_let_46 (_let_45))) (let ((_let_47 (REFL :args (_let_34)))) (let ((_let_48 (AND_ELIM _let_17 :args (2)))) (let ((_let_49 (_let_10))) (let ((_let_50 (ASSUME :args _let_49))) (let ((_let_51 (not _let_38))) (let ((_let_52 (_let_2))) (let ((_let_53 (ASSUME :args _let_52))) (let ((_let_54 (and _let_24 _let_51))) (let ((_let_55 (ASSUME :args (_let_51)))) (let ((_let_56 (ASSUME :args (_let_24)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_54)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_55 _let_56) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_56) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) :args (APPLY_UF ho_4)) (FALSE_INTRO _let_55))) :args (_let_51 _let_24))) :args (_let_24 _let_51))) :args (true _let_54)) (CONG (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_38))) (REFL :args ((not _let_36))) :args _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_ENUM)) :args _let_52)) _let_18 :args (_let_51 false _let_2)) (REORDERING (CNF_EQUIV_POS2 :args (_let_37)) :args ((or _let_36 (not _let_35) (not _let_37)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_49)) _let_48 :args (_let_37 false _let_10)) (REORDERING (CNF_AND_NEG :args (_let_35)) :args ((or _let_33 _let_31 _let_35))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_41)) :args ((or _let_30 _let_34))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_41)) :args ((or _let_32 _let_34))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_28))) (REFL :args ((not _let_34))) :args _let_41)) (CNF_EQUIV_NEG2 :args _let_44) _let_43 :args (_let_39 true _let_38 false _let_36 false _let_37 false _let_35 false _let_30 false _let_32 true _let_34 true _let_28 true _let_29)))) (let ((_let_58 (_let_25))) (let ((_let_59 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_416))) (let ((_let_60 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_416))) (let ((_let_61 (and _let_60 _let_59))) (let ((_let_62 (= _let_20 _let_61))) (let ((_let_63 (not _let_20))) (let ((_let_64 (not _let_59))) (let ((_let_65 (not _let_60))) (let ((_let_66 (or _let_65 _let_64))) (let ((_let_67 (not _let_61))) (let ((_let_68 (_let_28))) (let ((_let_69 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_416 QUANTIFIERS_INST_CBQI_CONFLICT))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args _let_69) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_21)) :args ((or _let_20 _let_3 _let_21))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or _let_63 _let_61 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_64 (not _let_66)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_68) :args _let_69) :args _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_44) :args ((or _let_24 _let_28 _let_29))) _let_57 _let_43 :args (_let_28 true _let_24 true _let_29)) :args (_let_66 false _let_28)) (REORDERING (CNF_AND_POS :args (_let_61 1)) :args ((or _let_59 _let_67))) (REORDERING (CNF_AND_POS :args (_let_61 0)) :args ((or _let_60 _let_67))) :args (_let_67 false _let_66 false _let_59 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_416 QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_670) BOUND_VARIABLE_667) BOUND_VARIABLE_647)))) :args _let_49)) _let_48 :args (_let_62 false _let_10)) :args (_let_63 true _let_61 false _let_62)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_22))) (REFL :args (_let_23)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_24 _let_25 (not _let_26)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_27) :args (_let_19 k_8 QUANTIFIERS_INST_ENUM)) :args _let_27))) (AND_ELIM _let_17 :args (7)) :args (_let_26 false _let_5)) :args (_let_25 true _let_24 false _let_26)) :args (_let_23 true _let_22)) :args (_let_3 true _let_20 true _let_21)) _let_18 :args (false false _let_3 false _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.79 )
% 0.20/0.79 % SZS output end Proof for SET636^5
% 0.20/0.79 % cvc5---1.0.5 exiting
% 0.20/0.80 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------