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