TSTP Solution File: SET595^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET595^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 14:39:18 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET595^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 08:51:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.47 %----Proving TH0
% 0.21/0.59 %------------------------------------------------------------------------------
% 0.21/0.59 % File : SET595^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.59 % Domain : Set Theory
% 0.21/0.59 % Problem : TPS problem BOOL-PROP-54
% 0.21/0.59 % Version : Especial.
% 0.21/0.59 % English : Trybulec's 54th Boolean property of sets
% 0.21/0.59
% 0.21/0.59 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.21/0.59 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.59 % Source : [Bro09]
% 0.21/0.59 % Names : tps_0219 [Bro09]
% 0.21/0.59 % : BOOL-PROP-54 [TPS]
% 0.21/0.59
% 0.21/0.59 % Status : Theorem
% 0.21/0.59 % Rating : 0.08 v8.1.0, 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, 0.00 v6.1.0, 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
% 0.21/0.59 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.21/0.59 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.21/0.59 % Maximal formula atoms : 1 ( 1 avg)
% 0.21/0.59 % Number of connectives : 10 ( 1 ~; 1 |; 1 &; 5 @)
% 0.21/0.59 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.59 % Maximal formula depth : 7 ( 7 avg)
% 0.21/0.59 % Number of types : 2 ( 1 usr)
% 0.21/0.59 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.59 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.59 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.21/0.59 % SPC : TH0_THM_EQU_NAR
% 0.21/0.59
% 0.21/0.59 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.59 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.59 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.59 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.59 % : Polymorphic definitions expanded.
% 0.21/0.59 %------------------------------------------------------------------------------
% 0.21/0.59 thf(a_type,type,
% 0.21/0.59 a: $tType ).
% 0.21/0.59
% 0.21/0.59 thf(cBOOL_PROP_54_pme,conjecture,
% 0.21/0.59 ! [X: a > $o,Y: a > $o] :
% 0.21/0.59 ( ! [Xx: a] :
% 0.21/0.59 ( ( X @ Xx )
% 0.21/0.59 => ( Y @ Xx ) )
% 0.21/0.59 => ( Y
% 0.21/0.59 = ( ^ [Xz: a] :
% 0.21/0.59 ( ( X @ Xz )
% 0.21/0.59 | ( ( Y @ Xz )
% 0.21/0.59 & ~ ( X @ Xz ) ) ) ) ) ) ).
% 0.21/0.59
% 0.21/0.59 %------------------------------------------------------------------------------
% 0.21/0.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.yuhG2KWiFJ/cvc5---1.0.5_2634.p...
% 0.21/0.59 (declare-sort $$unsorted 0)
% 0.21/0.59 (declare-sort tptp.a 0)
% 0.21/0.59 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (= Y (lambda ((Xz tptp.a)) (let ((_let_1 (@ X Xz))) (or _let_1 (and (@ Y Xz) (not _let_1))))))))))
% 0.21/0.59 (set-info :filename cvc5---1.0.5_2634)
% 0.21/0.59 (check-sat-assuming ( true ))
% 0.21/0.59 ------- get file name : TPTP file name is SET595^5
% 0.21/0.59 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2634.smt2...
% 0.21/0.59 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.59 % SZS status Theorem for SET595^5
% 0.21/0.59 % SZS output start Proof for SET595^5
% 0.21/0.59 (
% 0.21/0.59 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (= Y (lambda ((Xz tptp.a)) (let ((_let_1 (@ X Xz))) (or _let_1 (and (@ Y Xz) (not _let_1))))))))))) (let ((_let_2 (forall ((Xx tptp.a)) (or (not (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx)) (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx))))) (let ((_let_3 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85))) (let ((_let_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85))) (let ((_let_5 (not _let_4))) (let ((_let_6 (or _let_5 _let_3))) (let ((_let_7 (ho_6 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_7))) (let ((_let_9 (not _let_2))) (let ((_let_10 (or _let_9 _let_8))) (let ((_let_11 (forall ((BOUND_VARIABLE_666 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_667 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xx tptp.a)) (or (not (ho_3 BOUND_VARIABLE_666 Xx)) (ho_3 BOUND_VARIABLE_667 Xx)))) (= BOUND_VARIABLE_667 (ho_6 (ho_5 k_4 BOUND_VARIABLE_667) BOUND_VARIABLE_666)))))) (let ((_let_12 (not _let_10))) (let ((_let_13 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_14 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_15 (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_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_16 (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_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_17 (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_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_18 (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_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_19 (forall ((BOUND_VARIABLE_646 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_643 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_626 tptp.a)) (let ((_let_1 (ho_3 BOUND_VARIABLE_643 BOUND_VARIABLE_626))) (= (ho_3 (ho_6 (ho_5 k_4 BOUND_VARIABLE_646) BOUND_VARIABLE_643) BOUND_VARIABLE_626) (or _let_1 (and (ho_3 BOUND_VARIABLE_646 BOUND_VARIABLE_626) (not _let_1)))))))) (let ((_let_20 (not _let_11))) (let ((_let_21 (forall ((BOUND_VARIABLE_624 (-> tptp.a Bool)) (BOUND_VARIABLE_625 (-> tptp.a Bool)) (BOUND_VARIABLE_626 tptp.a)) (let ((_let_1 (@ BOUND_VARIABLE_625 BOUND_VARIABLE_626))) (= (or _let_1 (and (@ BOUND_VARIABLE_624 BOUND_VARIABLE_626) (not _let_1))) (ll_2 BOUND_VARIABLE_624 BOUND_VARIABLE_625 BOUND_VARIABLE_626)))))) (let ((_let_22 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (= Y (@ (@ ll_2 Y) X))))))) (let ((_let_23 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (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 (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (= Y (lambda ((Xz tptp.a)) (let ((_let_1 (@ X Xz))) (or _let_1 (and (@ Y Xz) (not _let_1))))))))) _let_22))))) (PREPROCESS :args (_let_21))) (PREPROCESS :args ((= (and _let_22 _let_21) (and _let_20 _let_19))))) (PREPROCESS :args ((and _let_18 _let_17 _let_16 _let_15 _let_14 _let_13)))) :args ((and _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13))))) (let ((_let_24 (or))) (let ((_let_25 (_let_20))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_25)) :args _let_25)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_11))) (REFL :args (_let_12)) :args _let_24)) (AND_ELIM _let_23 :args (0)) :args (_let_12 true _let_11)))) (let ((_let_27 (not _let_6))) (let ((_let_28 (and _let_3 _let_5))) (let ((_let_29 (or _let_4 _let_28))) (let ((_let_30 (ho_3 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (_let_19))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 QUANTIFIERS_INST_E_MATCHING ((ho_3 (ho_6 (ho_5 k_4 BOUND_VARIABLE_646) BOUND_VARIABLE_643) BOUND_VARIABLE_626)))) :args _let_32)) (AND_ELIM _let_23 :args (1)) :args (_let_31 false _let_19)))) (let ((_let_34 (= _let_3 _let_30))) (let ((_let_35 (forall ((z tptp.a)) (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 z) (ho_3 (ho_6 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) z))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (not _let_35))) (let ((_let_38 (or _let_37 _let_8))) (let ((_let_39 (_let_14))) (let ((_let_40 (_let_37))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_40)) :args _let_40)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_35))) (REFL :args (_let_36)) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_8 _let_37 (not _let_38)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_10 1)) _let_26 :args ((not _let_8) true _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_7 QUANTIFIERS_INST_ENUM)) :args _let_39)) (AND_ELIM _let_23 :args (6)) :args (_let_38 false _let_14)) :args (_let_37 true _let_8 false _let_38)) :args (_let_36 true _let_35)))) (let ((_let_42 (not _let_3))) (let ((_let_43 (_let_34))) (let ((_let_44 (not _let_31))) (let ((_let_45 (not _let_29))) (let ((_let_46 (_let_31))) (let ((_let_47 (_let_28))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_47) (CONG (REFL :args _let_47) (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_24)) :args ((or _let_42 _let_4 _let_28))) (CNF_OR_NEG :args (_let_29 1)) (REORDERING (CNF_OR_NEG :args (_let_29 0)) :args ((or _let_5 _let_29))) (REORDERING (CNF_EQUIV_POS2 :args _let_46) :args ((or _let_30 _let_45 _let_44))) _let_33 (CNF_EQUIV_NEG2 :args _let_43) _let_41 :args (_let_42 true _let_28 true _let_4 true _let_29 false _let_31 true _let_30 true _let_34)))) (let ((_let_49 (not _let_28))) (let ((_let_50 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_3 _let_5 _let_27))) _let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_4 _let_28 _let_45))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_28 0)) :args ((or _let_3 _let_49))) _let_48 :args (_let_49 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_46) :args ((or (not _let_30) _let_29 _let_44))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_43) :args ((or _let_3 _let_30 _let_34))) _let_48 _let_41 :args (_let_30 true _let_3 true _let_34)) _let_33 :args (_let_29 false _let_30 false _let_31)) :args (_let_4 true _let_28 false _let_29)) :args (_let_27 true _let_3 false _let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_10 0)) (CONG (REFL :args (_let_10)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_2))) :args _let_24)) :args ((or _let_2 _let_10))) _let_26 :args (_let_2 true _let_10)) :args (false true _let_6 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.65 )
% 0.21/0.65 % SZS output end Proof for SET595^5
% 0.21/0.65 % cvc5---1.0.5 exiting
% 0.21/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------