TSTP Solution File: SET624^5 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET624^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 14:39:34 EDT 2023
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET624^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n003.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 09:39:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 % File : SET624^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.53 % Domain : Set Theory
% 0.20/0.53 % Problem : TPS problem BOOL-PROP-100
% 0.20/0.53 % Version : Especial.
% 0.20/0.53 % English : Trybulec's 100th Boolean property of sets
% 0.20/0.53
% 0.20/0.53 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.53 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.53 % Source : [Bro09]
% 0.20/0.53 % Names : tps_0385 [Bro09]
% 0.20/0.53 % : BOOL-PROP-100 [TPS]
% 0.20/0.53
% 0.20/0.53 % Status : Theorem
% 0.20/0.53 % Rating : 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.20/0.53 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.53 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.53 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.53 % Number of connectives : 13 ( 0 ~; 2 |; 3 &; 7 @)
% 0.20/0.53 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.53 % Maximal formula depth : 9 ( 9 avg)
% 0.20/0.53 % Number of types : 2 ( 1 usr)
% 0.20/0.53 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.53 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.53 % Number of variables : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% 0.20/0.53 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.53
% 0.20/0.53 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.53 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.53 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.53 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.53 % : Polymorphic definitions expanded.
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 thf(a_type,type,
% 0.20/0.53 a: $tType ).
% 0.20/0.53
% 0.20/0.53 thf(cBOOL_PROP_100_pme,conjecture,
% 0.20/0.53 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.20/0.53 ( ? [Xx: a] :
% 0.20/0.53 ( ( X @ Xx )
% 0.20/0.53 & ( ( Y @ Xx )
% 0.20/0.53 | ( Z @ Xx ) ) )
% 0.20/0.53 <=> ( ? [Xx: a] :
% 0.20/0.53 ( ( X @ Xx )
% 0.20/0.53 & ( Y @ Xx ) )
% 0.20/0.53 | ? [Xx: a] :
% 0.20/0.53 ( ( X @ Xx )
% 0.20/0.53 & ( Z @ Xx ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.mxdFBOAcIF/cvc5---1.0.5_13108.p...
% 0.20/0.53 (declare-sort $$unsorted 0)
% 0.20/0.53 (declare-sort tptp.a 0)
% 0.20/0.53 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (= (exists ((Xx tptp.a)) (and (@ X Xx) (or (@ Y Xx) (@ Z Xx)))) (or (exists ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))) (exists ((Xx tptp.a)) (and (@ X Xx) (@ Z Xx))))))))
% 0.20/0.53 (set-info :filename cvc5---1.0.5_13108)
% 0.20/0.53 (check-sat-assuming ( true ))
% 0.20/0.53 ------- get file name : TPTP file name is SET624^5
% 0.20/0.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13108.smt2...
% 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for SET624^5
% 0.20/0.53 % SZS output start Proof for SET624^5
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (= (exists ((Xx tptp.a)) (and (@ X Xx) (or (@ Y Xx) (@ Z Xx)))) (or (exists ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))) (exists ((Xx tptp.a)) (and (@ X Xx) (@ Z Xx))))))))) (let ((_let_2 (forall ((Xx tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx)) (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx)))))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_4 (not _let_3))) (let ((_let_5 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_6 (not _let_5))) (let ((_let_7 (or _let_6 _let_4))) (let ((_let_8 (not _let_2))) (let ((_let_9 (forall ((Xx tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx)) (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)))))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_10 _let_8))) (let ((_let_12 (forall ((Xx tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx)) (and (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)) (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (= _let_11 _let_13))) (let ((_let_15 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_16 (not _let_15))) (let ((_let_17 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16))) (let ((_let_20 (and (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) _let_16))) (let ((_let_21 (or _let_18 _let_20))) (let ((_let_22 (or))) (let ((_let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_2))))) (let ((_let_24 (_let_11))) (let ((_let_25 (REFL :args _let_24))) (let ((_let_26 (forall ((BOUND_VARIABLE_640 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_646 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_635 |u_(-> tptp.a Bool)|)) (= (or (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_640 Xx)) (not (ho_2 BOUND_VARIABLE_646 Xx))))) (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_640 Xx)) (not (ho_2 BOUND_VARIABLE_635 Xx)))))) (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_640 Xx)) (and (not (ho_2 BOUND_VARIABLE_646 Xx)) (not (ho_2 BOUND_VARIABLE_635 Xx)))))))))) (let ((_let_27 (not _let_14))) (let ((_let_28 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_29 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_30 (not _let_26))) (let ((_let_31 (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)) (Z (-> tptp.a Bool))) (= (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (and (not (@ Y Xx)) (not (@ Z Xx)))))) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (not (@ Y Xx))))) (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (not (@ Z Xx))))))))) _let_30))))))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_22)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_31 (PREPROCESS :args ((and _let_29 _let_28)))) :args ((and _let_30 _let_29 _let_28))) :args (0)) :args (_let_27 true _let_26)))) (let ((_let_33 (not _let_11))) (let ((_let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))))) (let ((_let_35 (_let_14))) (let ((_let_36 (REORDERING (EQ_RESOLVE (CNF_EQUIV_NEG2 :args _let_35) (CONG (REFL :args _let_35) (REFL :args (_let_33)) _let_34 :args _let_22)) :args ((or _let_12 _let_14 _let_33))))) (let ((_let_37 (_let_8))) (let ((_let_38 (REFL :args (_let_19)))) (let ((_let_39 (_let_12))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_18 _let_20 (not _let_21)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_39)) (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_16 (not _let_20)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 1)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_22)) :args ((or _let_15 _let_19))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 0)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_22)) :args ((or _let_17 _let_19))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_37)) :args _let_37)) (CONG _let_23 (REFL :args ((not _let_19))) :args _let_22)) _let_36 _let_32 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 1)) (CONG _let_25 _let_23 :args _let_22)) :args ((or _let_2 _let_11))) :args (_let_2 false _let_21 true _let_20 false _let_15 false _let_17 true _let_19 false _let_12 true _let_14 false _let_11)))) (let ((_let_42 (not _let_7))) (let ((_let_43 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_44 (not _let_43))) (let ((_let_45 (and _let_44 _let_4))) (let ((_let_46 (or _let_6 _let_45))) (let ((_let_47 (not _let_46))) (let ((_let_48 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_49 (not _let_48))) (let ((_let_50 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49))) (let ((_let_53 (and _let_49 (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_54 (or _let_51 _let_53))) (let ((_let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))))) (let ((_let_56 (_let_10))) (let ((_let_57 (REFL :args (_let_52)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_51 _let_53 (not _let_54)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_39)) (REORDERING (CNF_AND_POS :args (_let_53 0)) :args ((or _let_49 (not _let_53)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_22)) :args ((or _let_48 _let_52))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_22)) :args ((or _let_50 _let_52))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_56)) :args _let_56)) (CONG _let_55 (REFL :args ((not _let_52))) :args _let_22)) _let_36 _let_32 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG _let_25 _let_55 :args _let_22)) :args ((or _let_9 _let_11))) :args (_let_9 false _let_54 true _let_53 false _let_48 false _let_50 true _let_52 false _let_12 true _let_14 false _let_11)))) (let ((_let_59 (_let_13))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59)) (CONG _let_34 (REFL :args (_let_47)) :args _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_35) :args ((or _let_11 _let_13 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args _let_24) :args ((or _let_10 _let_8 _let_33))) _let_58 _let_41 :args (_let_33 false _let_9 false _let_2)) _let_32 :args (_let_13 true _let_11 true _let_14)) :args (_let_47 true _let_12)))) (let ((_let_61 (or _let_6 _let_44))) (let ((_let_62 (_let_9))) (let ((_let_63 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_22)) :args ((or _let_5 _let_46))) _let_60 :args (_let_5 true _let_46)))) (let ((_let_65 (_let_45))) (let ((_let_66 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_66) :args _let_63) :args _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_6 _let_4 _let_42))) _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_65) (CONG (REFL :args _let_65) (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) (MACRO_SR_PRED_INTRO :args ((= (not _let_4) _let_3))) :args _let_22)) :args ((or _let_43 _let_3 _let_45))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_6 _let_44 (not _let_61)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_62) :args _let_63) :args _let_62)) _let_58 :args (_let_61 false _let_9)) :args (_let_44 false _let_5 false _let_61)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 1)) _let_60 :args ((not _let_45) true _let_46)) :args (_let_3 true _let_43 true _let_45)) :args (_let_42 false _let_5 false _let_3)) _let_41 :args (false true _let_7 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.54 )
% 0.20/0.54 % SZS output end Proof for SET624^5
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------