TSTP Solution File: SEV222^5 by cvc5---1.0.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEV222^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n012.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 19:21:54 EDT 2023

% Result   : Theorem 0.18s 0.49s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEV222^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.33  % Computer : n012.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Thu Aug 24 02:26:57 EDT 2023
% 0.13/0.33  % CPUTime    : 
% 0.18/0.46  %----Proving TH0
% 0.18/0.49  %------------------------------------------------------------------------------
% 0.18/0.49  % File     : SEV222^5 : TPTP v8.1.2. Released v4.0.0.
% 0.18/0.49  % Domain   : Set Theory (Sets of sets)
% 0.18/0.49  % Problem  : TPS problem THM60
% 0.18/0.49  % Version  : Especial.
% 0.18/0.49  % English  :
% 0.18/0.49  
% 0.18/0.49  % Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.49  % Source   : [Bro09]
% 0.18/0.49  % Names    : tps_0460 [Bro09]
% 0.18/0.49  %          : THM60 [TPS]
% 0.18/0.49  
% 0.18/0.49  % Status   : Theorem
% 0.18/0.49  % Rating   : 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.18/0.49  % Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
% 0.18/0.49  %            Number of atoms       :    5 (   1 equ;   0 cnn)
% 0.18/0.49  %            Maximal formula atoms :    4 (   5 avg)
% 0.18/0.49  %            Number of connectives :   13 (   0   ~;   2   |;   1   &;   7   @)
% 0.18/0.49  %                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
% 0.18/0.49  %            Maximal formula depth :    8 (   8 avg)
% 0.18/0.49  %            Number of types       :    2 (   1 usr)
% 0.18/0.49  %            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
% 0.18/0.49  %            Number of symbols     :    3 (   2 usr;   0 con; 1-2 aty)
% 0.18/0.49  %            Number of variables   :    5 (   1   ^;   3   !;   1   ?;   5   :)
% 0.18/0.49  % SPC      : TH0_THM_EQU_NAR
% 0.18/0.49  
% 0.18/0.49  % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.49  %            project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.49  %            Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.49  %            license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.49  %          : Polymorphic definitions expanded.
% 0.18/0.49  %------------------------------------------------------------------------------
% 0.18/0.49  thf(a_type,type,
% 0.18/0.49      a: $tType ).
% 0.18/0.49  
% 0.18/0.49  thf(cZ,type,
% 0.18/0.49      cZ: a > $o ).
% 0.18/0.49  
% 0.18/0.49  thf(cW,type,
% 0.18/0.49      cW: ( a > $o ) > $o ).
% 0.18/0.49  
% 0.18/0.49  thf(cTHM60_pme,conjecture,
% 0.18/0.49      ! [Xx: a] :
% 0.18/0.49        ( ( ! [S: a > $o] :
% 0.18/0.49              ( ( cW @ S )
% 0.18/0.49             => ( S @ Xx ) )
% 0.18/0.49          | ( cZ @ Xx ) )
% 0.18/0.49      <=> ! [S: a > $o] :
% 0.18/0.49            ( ? [Xt: a > $o] :
% 0.18/0.49                ( ( cW @ Xt )
% 0.18/0.49                & ( S
% 0.18/0.49                  = ( ^ [Xz: a] :
% 0.18/0.49                        ( ( cZ @ Xz )
% 0.18/0.49                        | ( Xt @ Xz ) ) ) ) )
% 0.18/0.49           => ( S @ Xx ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  %------------------------------------------------------------------------------
% 0.18/0.49  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.7l2YwCefJA/cvc5---1.0.5_12641.p...
% 0.18/0.49  (declare-sort $$unsorted 0)
% 0.18/0.49  (declare-sort tptp.a 0)
% 0.18/0.49  (declare-fun tptp.cZ (tptp.a) Bool)
% 0.18/0.49  (declare-fun tptp.cW ((-> tptp.a Bool)) Bool)
% 0.18/0.49  (assert (not (forall ((Xx tptp.a)) (= (or (forall ((S (-> tptp.a Bool))) (=> (@ tptp.cW S) (@ S Xx))) (@ tptp.cZ Xx)) (forall ((S (-> tptp.a Bool))) (=> (exists ((Xt (-> tptp.a Bool))) (and (@ tptp.cW Xt) (= S (lambda ((Xz tptp.a)) (or (@ tptp.cZ Xz) (@ Xt Xz)))))) (@ S Xx)))))))
% 0.18/0.49  (set-info :filename cvc5---1.0.5_12641)
% 0.18/0.49  (check-sat-assuming ( true ))
% 0.18/0.49  ------- get file name : TPTP file name is SEV222^5
% 0.18/0.49  ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12641.smt2...
% 0.18/0.49  --- Run --ho-elim --full-saturate-quant at 10...
% 0.18/0.49  % SZS status Theorem for SEV222^5
% 0.18/0.49  % SZS output start Proof for SEV222^5
% 0.18/0.49  (
% 0.18/0.49  (let ((_let_1 (not (forall ((Xx tptp.a)) (= (or (forall ((S (-> tptp.a Bool))) (=> (@ tptp.cW S) (@ S Xx))) (@ tptp.cZ Xx)) (forall ((S (-> tptp.a Bool))) (=> (exists ((Xt (-> tptp.a Bool))) (and (@ tptp.cW Xt) (= S (lambda ((Xz tptp.a)) (or (@ tptp.cZ Xz) (@ Xt Xz)))))) (@ S Xx)))))))) (let ((_let_2 (ho_2 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_3 (forall ((BOUND_VARIABLE_674 |u_(-> tptp.a Bool)|)) (or (not (ho_4 k_3 BOUND_VARIABLE_674)) (ho_2 BOUND_VARIABLE_674 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_4 (or _let_3 _let_2))) (let ((_let_5 (forall ((BOUND_VARIABLE_657 |u_(-> tptp.a Bool)|)) (or (not (ho_4 k_3 BOUND_VARIABLE_657)) (ho_2 BOUND_VARIABLE_657 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_6 (or _let_2 _let_5))) (let ((_let_7 (= _let_6 _let_4))) (let ((_let_8 (forall ((Xx tptp.a)) (let ((_let_1 (ho_2 k_5 Xx))) (= (or _let_1 (forall ((BOUND_VARIABLE_657 |u_(-> tptp.a Bool)|)) (or (not (ho_4 k_3 BOUND_VARIABLE_657)) (ho_2 BOUND_VARIABLE_657 Xx)))) (or (forall ((BOUND_VARIABLE_674 |u_(-> tptp.a Bool)|)) (or (not (ho_4 k_3 BOUND_VARIABLE_674)) (ho_2 BOUND_VARIABLE_674 Xx))) _let_1)))))) (let ((_let_9 (not _let_7))) (let ((_let_10 (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_11 (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_12 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_13 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_14 (not _let_8))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xx tptp.a)) (let ((_let_1 (@ tptp.cZ Xx))) (= (or (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cW S)) (@ S Xx))) _let_1) (or _let_1 (forall ((BOUND_VARIABLE_624 (-> tptp.a Bool))) (or (not (@ tptp.cW BOUND_VARIABLE_624)) (@ BOUND_VARIABLE_624 Xx)))))))) _let_14))))))) (let ((_let_16 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_15) :args (_let_14))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_8))) (REFL :args (_let_9)) :args (or))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_15 (PREPROCESS :args ((and _let_13 _let_12 _let_11 _let_10)))) :args ((and _let_14 _let_13 _let_12 _let_11 _let_10))) :args (0)) :args (_let_9 true _let_8)))) (let ((_let_17 (not _let_6))) (let ((_let_18 (not _let_5))) (let ((_let_19 (ALPHA_EQUIV :args (_let_5 (= BOUND_VARIABLE_657 BOUND_VARIABLE_674))))) (let ((_let_20 (_let_7))) (let ((_let_21 (CNF_EQUIV_NEG2 :args _let_20))) (let ((_let_22 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_4 0)) _let_21 _let_16 (REORDERING (EQUIV_ELIM1 _let_19) :args ((or _let_3 _let_18))) (CNF_OR_NEG :args (_let_6 1)) :args (_let_18 true _let_4 true _let_7 false _let_3 false _let_6)))) (let ((_let_23 (MACRO_RESOLUTION_TRUST _let_21 _let_16 (CNF_OR_NEG :args (_let_4 1)) (CNF_OR_NEG :args (_let_6 0)) :args ((not _let_2) true _let_7 false _let_4 false _let_6)))) (let ((_let_24 (not _let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_20) :args ((or _let_6 _let_4 _let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_4)) :args ((or _let_2 _let_3 _let_24))) _let_23 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_19) _let_22 :args ((not _let_3) true _let_5)) :args (_let_24 true _let_2 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_2 _let_5 _let_17))) _let_23 _let_22 :args (_let_17 true _let_2 true _let_5)) _let_16 :args (false true _let_4 true _let_6 true _let_7)) :args (_let_1 true)))))))))))))))))))))))))))
% 0.18/0.49  )
% 0.18/0.49  % SZS output end Proof for SEV222^5
% 0.18/0.49  % cvc5---1.0.5 exiting
% 0.18/0.50  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------