TSTP Solution File: SET616^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET616^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 14:39:30 EDT 2023
% Result : Theorem 0.21s 0.57s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET616^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n031.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 : Sat Aug 26 09:52:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.57 %------------------------------------------------------------------------------
% 0.21/0.57 % File : SET616^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.57 % Domain : Set Theory
% 0.21/0.57 % Problem : TPS problem BOOL-PROP-90
% 0.21/0.57 % Version : Especial.
% 0.21/0.57 % English : Trybulec's 90th Boolean property of sets
% 0.21/0.57
% 0.21/0.57 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.21/0.57 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.57 % Source : [Bro09]
% 0.21/0.57 % Names : tps_0288 [Bro09]
% 0.21/0.57 % : BOOL-PROP-90 [TPS]
% 0.21/0.57
% 0.21/0.57 % Status : Theorem
% 0.21/0.57 % Rating : 0.15 v8.1.0, 0.18 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 v6.0.0, 0.29 v5.5.0, 0.33 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
% 0.21/0.57 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.21/0.57 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.21/0.57 % Maximal formula atoms : 2 ( 2 avg)
% 0.21/0.57 % Number of connectives : 9 ( 2 ~; 0 |; 2 &; 4 @)
% 0.21/0.57 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.57 % Maximal formula depth : 4 ( 4 avg)
% 0.21/0.57 % Number of types : 2 ( 1 usr)
% 0.21/0.57 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.57 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.57 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.21/0.57 % SPC : TH0_THM_EQU_NAR
% 0.21/0.57
% 0.21/0.57 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.57 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.57 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.57 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.57 % : Polymorphic definitions expanded.
% 0.21/0.57 %------------------------------------------------------------------------------
% 0.21/0.57 thf(a_type,type,
% 0.21/0.57 a: $tType ).
% 0.21/0.57
% 0.21/0.57 thf(cBOOL_PROP_90_pme,conjecture,
% 0.21/0.57 ! [X: a > $o,Y: a > $o] :
% 0.21/0.57 ( ( ( ^ [Xx: a] :
% 0.21/0.57 ( ( X @ Xx )
% 0.21/0.57 & ~ ( Y @ Xx ) ) )
% 0.21/0.57 = ( ^ [Xx: a] :
% 0.21/0.57 ( ( Y @ Xx )
% 0.21/0.57 & ~ ( X @ Xx ) ) ) )
% 0.21/0.57 => ( X = Y ) ) ).
% 0.21/0.57
% 0.21/0.57 %------------------------------------------------------------------------------
% 0.21/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.BWrXPgqZzL/cvc5---1.0.5_6817.p...
% 0.21/0.57 (declare-sort $$unsorted 0)
% 0.21/0.57 (declare-sort tptp.a 0)
% 0.21/0.57 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (= (lambda ((Xx tptp.a)) (and (@ X Xx) (not (@ Y Xx)))) (lambda ((Xx tptp.a)) (and (@ Y Xx) (not (@ X Xx))))) (= X Y)))))
% 0.21/0.57 (set-info :filename cvc5---1.0.5_6817)
% 0.21/0.57 (check-sat-assuming ( true ))
% 0.21/0.57 ------- get file name : TPTP file name is SET616^5
% 0.21/0.57 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_6817.smt2...
% 0.21/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.57 % SZS status Theorem for SET616^5
% 0.21/0.57 % SZS output start Proof for SET616^5
% 0.21/0.57 (
% 0.21/0.57 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (= (lambda ((Xx tptp.a)) (and (@ X Xx) (not (@ Y Xx)))) (lambda ((Xx tptp.a)) (and (@ Y Xx) (not (@ X Xx))))) (= X Y)))))) (let ((_let_2 (ho_7 (ho_6 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_3 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_4 (= _let_3 _let_2))) (let ((_let_5 (ho_4 _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_6 (ho_4 _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_8 (not _let_4))) (let ((_let_9 (or _let_8 _let_7))) (let ((_let_10 (forall ((BOUND_VARIABLE_709 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_708 |u_(-> tptp.a Bool)|)) (or (not (= (ho_7 (ho_6 k_5 BOUND_VARIABLE_709) BOUND_VARIABLE_708) (ho_7 (ho_6 k_8 BOUND_VARIABLE_708) BOUND_VARIABLE_709))) (= BOUND_VARIABLE_708 BOUND_VARIABLE_709))))) (let ((_let_11 (not _let_9))) (let ((_let_12 (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_13 (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_14 (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_15 (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_16 (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_17 (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_18 (forall ((BOUND_VARIABLE_673 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_670 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_649 tptp.a)) (= (ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_673) BOUND_VARIABLE_670) BOUND_VARIABLE_649) (and (ho_4 BOUND_VARIABLE_673 BOUND_VARIABLE_649) (not (ho_4 BOUND_VARIABLE_670 BOUND_VARIABLE_649))))))) (let ((_let_19 (forall ((BOUND_VARIABLE_696 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_695 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_638 tptp.a)) (= (ho_4 (ho_7 (ho_6 k_8 BOUND_VARIABLE_696) BOUND_VARIABLE_695) BOUND_VARIABLE_638) (and (ho_4 BOUND_VARIABLE_696 BOUND_VARIABLE_638) (not (ho_4 BOUND_VARIABLE_695 BOUND_VARIABLE_638))))))) (let ((_let_20 (not _let_10))) (let ((_let_21 (forall ((BOUND_VARIABLE_647 (-> tptp.a Bool)) (BOUND_VARIABLE_648 (-> tptp.a Bool)) (BOUND_VARIABLE_649 tptp.a)) (= (and (@ BOUND_VARIABLE_647 BOUND_VARIABLE_649) (not (@ BOUND_VARIABLE_648 BOUND_VARIABLE_649))) (ll_3 BOUND_VARIABLE_647 BOUND_VARIABLE_648 BOUND_VARIABLE_649))))) (let ((_let_22 (forall ((BOUND_VARIABLE_636 (-> tptp.a Bool)) (BOUND_VARIABLE_637 (-> tptp.a Bool)) (BOUND_VARIABLE_638 tptp.a)) (= (and (@ BOUND_VARIABLE_636 BOUND_VARIABLE_638) (not (@ BOUND_VARIABLE_637 BOUND_VARIABLE_638))) (ll_2 BOUND_VARIABLE_636 BOUND_VARIABLE_637 BOUND_VARIABLE_638))))) (let ((_let_23 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (or (not (= (@ (@ ll_2 Y) X) (@ (@ ll_3 X) Y))) (= X Y)))))) (let ((_let_24 (and _let_23 _let_22 _let_21))) (let ((_let_25 (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))) (or (not (= (lambda ((Xx tptp.a)) (and (@ X Xx) (not (@ Y Xx)))) (lambda ((Xx tptp.a)) (and (@ Y Xx) (not (@ X Xx)))))) (= X Y)))) _let_23))))) (PREPROCESS :args ((and _let_22 _let_21)))) :args (_let_24)) (PREPROCESS :args ((= _let_24 (and _let_20 _let_19 _let_18))))) (PREPROCESS :args ((and _let_17 _let_16 _let_15 _let_14 _let_13 _let_12)))) :args ((and _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12))))) (let ((_let_26 (or))) (let ((_let_27 (_let_20))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_27)) :args _let_27) (REWRITE :args ((=> _let_20 (not (or _let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_10))) (REFL :args (_let_11)) :args _let_26)) (AND_ELIM _let_25 :args (0)) :args (_let_11 true _let_10)))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 0)) (CONG (REFL :args (_let_9)) (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_4))) :args _let_26)) :args ((or _let_4 _let_9))) _let_28 :args (_let_4 true _let_9)))) (let ((_let_30 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_31 (not _let_30))) (let ((_let_32 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_33 (and _let_32 _let_31))) (let ((_let_34 (= _let_5 _let_33))) (let ((_let_35 (not _let_5))) (let ((_let_36 (_let_18))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_36) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_36)) (AND_ELIM _let_25 :args (2)) :args (_let_34 false _let_18)))) (let ((_let_38 (not _let_33))) (let ((_let_39 (= _let_32 _let_30))) (let ((_let_40 (not _let_32))) (let ((_let_41 (and _let_30 _let_40))) (let ((_let_42 (= _let_6 _let_41))) (let ((_let_43 (forall ((z tptp.a)) (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 z) (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 z))))) (let ((_let_44 (not _let_39))) (let ((_let_45 (not _let_43))) (let ((_let_46 (or _let_45 _let_7))) (let ((_let_47 (_let_13))) (let ((_let_48 (_let_45))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_48)) :args _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_43))) (REFL :args (_let_44)) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_7 _let_45 (not _let_46)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_9 1)) _let_28 :args ((not _let_7) true _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_47) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_ENUM)) :args _let_47)) (AND_ELIM _let_25 :args (7)) :args (_let_46 false _let_13)) :args (_let_45 true _let_7 false _let_46)) :args (_let_44 true _let_43)))) (let ((_let_50 (_let_39))) (let ((_let_51 (not _let_41))) (let ((_let_52 (_let_33))) (let ((_let_53 (_let_19))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_53) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53)) (AND_ELIM _let_25 :args (1)) :args (_let_42 false _let_19)))) (let ((_let_55 (not _let_42))) (let ((_let_56 (not _let_6))) (let ((_let_57 (_let_42))) (let ((_let_58 (not _let_34))) (let ((_let_59 (_let_34))) (let ((_let_60 (_let_35))) (let ((_let_61 (REFL :args (_let_8)))) (let ((_let_62 (and _let_4 _let_56))) (let ((_let_63 (_let_56))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (APPLY_UF ho_4))) (let ((_let_66 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32)))) (let ((_let_67 (ASSUME :args (_let_4)))) (let ((_let_68 (SYMM _let_67))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_62)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_64 _let_67) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_68) _let_66 :args _let_65) (FALSE_INTRO _let_64))) :args (_let_56 _let_4))) :args (_let_4 _let_56))) :args (true _let_62)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_6))) (REFL :args _let_60) :args _let_26)) _let_29 (REORDERING (CNF_EQUIV_POS2 :args _let_59) :args ((or _let_5 _let_38 _let_58))) _let_37 (REORDERING (CNF_EQUIV_POS1 :args _let_57) :args ((or _let_41 _let_56 _let_55))) _let_54 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_52) (CONG (REFL :args _let_52) (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_26)) :args ((or _let_30 _let_40 _let_33))) (REORDERING (CNF_AND_POS :args (_let_41 1)) :args ((or _let_40 _let_51))) (CNF_EQUIV_NEG2 :args _let_50) _let_49 :args (_let_40 false _let_4 false _let_5 false _let_34 true _let_6 false _let_42 false _let_33 true _let_41 true _let_30 true _let_39)))) (let ((_let_70 (_let_41))) (let ((_let_71 (and _let_4 _let_35))) (let ((_let_72 (ASSUME :args _let_60))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_71)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_67) (SCOPE (FALSE_ELIM (TRANS (CONG _let_68 _let_66 :args _let_65) (FALSE_INTRO _let_72))) :args (_let_35 _let_4))) :args (_let_4 _let_35))) :args (true _let_71)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_5))) (REFL :args _let_63) :args _let_26)) :args ((or _let_8 _let_56 _let_5))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_57) :args ((or _let_6 _let_51 _let_55))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_70) (CONG (REFL :args _let_70) (REFL :args (_let_31)) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_32))) :args _let_26)) :args ((or _let_32 _let_31 _let_41))) _let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_50) :args ((or _let_32 _let_30 _let_39))) _let_69 _let_49 :args (_let_30 true _let_32 true _let_39)) :args (_let_41 true _let_32 false _let_30)) _let_54 :args (_let_6 false _let_41 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_59) :args ((or _let_33 _let_35 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_33 0)) :args ((or _let_32 _let_38))) _let_69 :args (_let_38 true _let_32)) _let_37 :args (_let_35 true _let_33 false _let_34)) _let_29 :args (false false _let_6 true _let_5 false _let_4)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.57 )
% 0.21/0.57 % SZS output end Proof for SET616^5
% 0.21/0.57 % cvc5---1.0.5 exiting
% 0.21/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------