TSTP Solution File: SEV220^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV220^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 19:21:53 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV220^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 04:04:40 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : SEV220^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.53 % Domain : Set Theory (Sets of sets)
% 0.21/0.53 % Problem : TPS problem X5205
% 0.21/0.53 % Version : Especial.
% 0.21/0.53 % English :
% 0.21/0.53
% 0.21/0.53 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.53 % Source : [Bro09]
% 0.21/0.53 % Names : tps_0322 [Bro09]
% 0.21/0.53 % : THM86 [TPS]
% 0.21/0.53 % : X5205 [TPS]
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % Rating : 0.15 v8.1.0, 0.09 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 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.21/0.53 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.21/0.53 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 4 ( 5 avg)
% 0.21/0.53 % Number of connectives : 13 ( 0 ~; 0 |; 3 &; 7 @)
% 0.21/0.53 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 8 ( 8 avg)
% 0.21/0.53 % Number of types : 3 ( 2 usr)
% 0.21/0.53 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.21/0.53 % Number of variables : 7 ( 1 ^; 3 !; 3 ?; 7 :)
% 0.21/0.53 % SPC : TH0_THM_EQU_NAR
% 0.21/0.53
% 0.21/0.53 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.53 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.53 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.53 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.53 % : Polymorphic definitions expanded.
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 thf(b_type,type,
% 0.21/0.53 b: $tType ).
% 0.21/0.53
% 0.21/0.53 thf(a_type,type,
% 0.21/0.53 a: $tType ).
% 0.21/0.53
% 0.21/0.53 thf(f,type,
% 0.21/0.53 f: b > a ).
% 0.21/0.53
% 0.21/0.53 thf(w,type,
% 0.21/0.53 w: ( b > $o ) > $o ).
% 0.21/0.53
% 0.21/0.53 thf(cX5205_pme,conjecture,
% 0.21/0.53 ! [Xx: a] :
% 0.21/0.53 ( ? [Xt: b] :
% 0.21/0.53 ( ! [S: b > $o] :
% 0.21/0.53 ( ( w @ S )
% 0.21/0.53 => ( S @ Xt ) )
% 0.21/0.53 & ( Xx
% 0.21/0.53 = ( f @ Xt ) ) )
% 0.21/0.53 => ! [S: a > $o] :
% 0.21/0.53 ( ? [Xt: b > $o] :
% 0.21/0.53 ( ( w @ Xt )
% 0.21/0.53 & ( S
% 0.21/0.53 = ( ^ [Xz: a] :
% 0.21/0.53 ? [Xt0: b] :
% 0.21/0.53 ( ( Xt @ Xt0 )
% 0.21/0.53 & ( Xz
% 0.21/0.53 = ( f @ Xt0 ) ) ) ) ) )
% 0.21/0.53 => ( S @ Xx ) ) ) ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XGEexJxw0D/cvc5---1.0.5_6861.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-sort tptp.b 0)
% 0.21/0.53 (declare-sort tptp.a 0)
% 0.21/0.53 (declare-fun tptp.f (tptp.b) tptp.a)
% 0.21/0.53 (declare-fun tptp.w ((-> tptp.b Bool)) Bool)
% 0.21/0.53 (assert (not (forall ((Xx tptp.a)) (=> (exists ((Xt tptp.b)) (and (forall ((S (-> tptp.b Bool))) (=> (@ tptp.w S) (@ S Xt))) (= Xx (@ tptp.f Xt)))) (forall ((S (-> tptp.a Bool))) (=> (exists ((Xt (-> tptp.b Bool))) (and (@ tptp.w Xt) (= S (lambda ((Xz tptp.a)) (exists ((Xt0 tptp.b)) (and (@ Xt Xt0) (= Xz (@ tptp.f Xt0)))))))) (@ S Xx)))))))
% 0.21/0.53 (set-info :filename cvc5---1.0.5_6861)
% 0.21/0.53 (check-sat-assuming ( true ))
% 0.21/0.53 ------- get file name : TPTP file name is SEV220^5
% 0.21/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_6861.smt2...
% 0.21/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for SEV220^5
% 0.21/0.53 % SZS output start Proof for SEV220^5
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (not (forall ((Xx tptp.a)) (=> (exists ((Xt tptp.b)) (and (forall ((S (-> tptp.b Bool))) (=> (@ tptp.w S) (@ S Xt))) (= Xx (@ tptp.f Xt)))) (forall ((S (-> tptp.a Bool))) (=> (exists ((Xt (-> tptp.b Bool))) (and (@ tptp.w Xt) (= S (lambda ((Xz tptp.a)) (exists ((Xt0 tptp.b)) (and (@ Xt Xt0) (= Xz (@ tptp.f Xt0)))))))) (@ S Xx)))))))) (let ((_let_2 (forall ((Xt0 tptp.b)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xt0)) (not (= (ho_6 k_5 Xt0) (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_4 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_5 (not _let_4))) (let ((_let_6 (not _let_2))) (let ((_let_7 (forall ((BOUND_VARIABLE_760 |u_(-> tptp.b Bool)|)) (or (not (ho_4 k_3 BOUND_VARIABLE_760)) (ho_2 BOUND_VARIABLE_760 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) (let ((_let_8 (not _let_7))) (let ((_let_9 (or _let_8 _let_6 _let_5))) (let ((_let_10 (forall ((BOUND_VARIABLE_737 |u_(-> tptp.b Bool)|) (BOUND_VARIABLE_692 tptp.b)) (or (not (forall ((BOUND_VARIABLE_760 |u_(-> tptp.b Bool)|)) (or (not (ho_4 k_3 BOUND_VARIABLE_760)) (ho_2 BOUND_VARIABLE_760 BOUND_VARIABLE_692)))) (not (forall ((Xt0 tptp.b)) (or (not (ho_2 BOUND_VARIABLE_737 Xt0)) (not (= (ho_6 k_5 BOUND_VARIABLE_692) (ho_6 k_5 Xt0)))))) (not (ho_4 k_3 BOUND_VARIABLE_737)))))) (let ((_let_11 (not _let_9))) (let ((_let_12 (forall ((u |u_(-> tptp.b Bool)|) (e Bool) (i tptp.b)) (not (forall ((v |u_(-> tptp.b Bool)|)) (not (forall ((ii tptp.b)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_13 (forall ((x |u_(-> tptp.b Bool)|) (y |u_(-> tptp.b Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_14 (forall ((u |u_(-> _u_(-> tptp.b Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.b Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.b Bool)|)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_15 (forall ((x |u_(-> _u_(-> tptp.b Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.b Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.b Bool)|)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_16 (forall ((u |u_(-> tptp.b tptp.a)|) (e tptp.a) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.a)|)) (not (forall ((ii tptp.b)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_17 (forall ((x |u_(-> tptp.b tptp.a)|) (y |u_(-> tptp.b tptp.a)|)) (or (not (forall ((z tptp.b)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_18 (not _let_10))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((BOUND_VARIABLE_702 (-> tptp.b Bool)) (BOUND_VARIABLE_692 tptp.b)) (or (not (forall ((S (-> tptp.b Bool))) (or (not (@ tptp.w S)) (@ S BOUND_VARIABLE_692)))) (not (forall ((Xt0 tptp.b)) (or (not (@ BOUND_VARIABLE_702 Xt0)) (not (= (@ tptp.f Xt0) (@ tptp.f BOUND_VARIABLE_692)))))) (not (@ tptp.w BOUND_VARIABLE_702))))) _let_18))))))) (let ((_let_20 (or))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_19) :args (_let_18)) (REWRITE :args ((=> _let_18 (not (or _let_8 (not (forall ((Xt0 tptp.b)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xt0)) (not (= (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) (ho_6 k_5 Xt0)))))) _let_5))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_10))) (REFL :args (_let_11)) :args _let_20)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_19 (PREPROCESS :args ((and _let_17 _let_16 _let_15 _let_14 _let_13 _let_12)))) :args ((and _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12))) :args (0)) :args (_let_11 true _let_10)))) (let ((_let_22 (REFL :args (_let_9)))) (let ((_let_23 (or _let_5 _let_3))) (let ((_let_24 (_let_7))) (let ((_let_25 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_25) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xt0) false))))) :args _let_25))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_5 _let_3 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 2)) (CONG _let_22 (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_20)) :args ((or _let_4 _let_9))) _let_21 :args (_let_4 true _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_24) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_4 k_3 BOUND_VARIABLE_760) false))))) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 0)) (CONG _let_22 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_20)) :args ((or _let_7 _let_9))) _let_21 :args (_let_7 true _let_9)) :args (_let_23 false _let_7)) :args (_let_3 false _let_4 false _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 1)) (CONG _let_22 (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_2))) :args _let_20)) :args ((or _let_2 _let_9))) _let_21 :args (_let_2 true _let_9)) :args (false false _let_3 false _let_2)) :args (_let_1 true))))))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for SEV220^5
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------