TSTP Solution File: SEV067^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV067^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 19:21:28 EDT 2023
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV067^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 04:17:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 % File : SEV067^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.52 % Domain : Set Theory (Relations)
% 0.20/0.52 % Problem : TPS problem THM553
% 0.20/0.52 % Version : Especial.
% 0.20/0.52 % English : Downward closed subsets of a linear order are comparable.
% 0.20/0.52
% 0.20/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.52 % Source : [Bro09]
% 0.20/0.52 % Names : tps_0441 [Bro09]
% 0.20/0.52 % : THM553 [TPS]
% 0.20/0.52
% 0.20/0.52 % Status : Theorem
% 0.20/0.52 % Rating : 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 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 v4.0.1, 0.33 v4.0.0
% 0.20/0.52 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.20/0.52 % Number of atoms : 19 ( 1 equ; 0 cnn)
% 0.20/0.52 % Maximal formula atoms : 19 ( 19 avg)
% 0.20/0.52 % Number of connectives : 46 ( 0 ~; 2 |; 9 &; 28 @)
% 0.20/0.52 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.52 % Maximal formula depth : 13 ( 13 avg)
% 0.20/0.52 % Number of types : 2 ( 1 usr)
% 0.20/0.52 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.52 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.20/0.52 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.20/0.52 % SPC : TH0_THM_EQU_NAR
% 0.20/0.52
% 0.20/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.52 % : Polymorphic definitions expanded.
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 thf(a_type,type,
% 0.20/0.52 a: $tType ).
% 0.20/0.52
% 0.20/0.52 thf(cS,type,
% 0.20/0.52 cS: a > $o ).
% 0.20/0.52
% 0.20/0.52 thf(cT,type,
% 0.20/0.52 cT: a > $o ).
% 0.20/0.52
% 0.20/0.52 thf(cR,type,
% 0.20/0.52 cR: a > a > $o ).
% 0.20/0.52
% 0.20/0.52 thf(cTHM553_pme,conjecture,
% 0.20/0.52 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.20/0.52 ( ( ( cR @ Xx @ Xy )
% 0.20/0.52 & ( cR @ Xy @ Xz ) )
% 0.20/0.52 => ( cR @ Xx @ Xz ) )
% 0.20/0.52 & ! [Xx: a] : ( cR @ Xx @ Xx )
% 0.20/0.52 & ! [Xx: a,Xy: a] :
% 0.20/0.52 ( ( ( cR @ Xx @ Xy )
% 0.20/0.52 & ( cR @ Xy @ Xx ) )
% 0.20/0.52 => ( Xx = Xy ) )
% 0.20/0.52 & ! [Xx: a,Xy: a] :
% 0.20/0.52 ( ( cR @ Xx @ Xy )
% 0.20/0.52 | ( cR @ Xy @ Xx ) )
% 0.20/0.52 & ! [Xu: a,Xv: a] :
% 0.20/0.52 ( ( ( cR @ Xu @ Xv )
% 0.20/0.52 & ( cS @ Xv ) )
% 0.20/0.52 => ( cS @ Xu ) )
% 0.20/0.52 & ! [Xu: a,Xv: a] :
% 0.20/0.52 ( ( ( cR @ Xu @ Xv )
% 0.20/0.52 & ( cT @ Xv ) )
% 0.20/0.52 => ( cT @ Xu ) ) )
% 0.20/0.52 => ( ! [Xx: a] :
% 0.20/0.52 ( ( cS @ Xx )
% 0.20/0.52 => ( cT @ Xx ) )
% 0.20/0.52 | ! [Xx: a] :
% 0.20/0.52 ( ( cT @ Xx )
% 0.20/0.52 => ( cS @ Xx ) ) ) ) ).
% 0.20/0.52
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.cPTv8CZo3a/cvc5---1.0.5_16470.p...
% 0.20/0.52 (declare-sort $$unsorted 0)
% 0.20/0.52 (declare-sort tptp.a 0)
% 0.20/0.52 (declare-fun tptp.cS (tptp.a) Bool)
% 0.20/0.52 (declare-fun tptp.cT (tptp.a) Bool)
% 0.20/0.52 (declare-fun tptp.cR (tptp.a tptp.a) Bool)
% 0.20/0.52 (assert (not (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ tptp.cR Xx))) (=> (and (@ _let_1 Xy) (@ (@ tptp.cR Xy) Xz)) (@ _let_1 Xz)))) (forall ((Xx tptp.a)) (@ (@ tptp.cR Xx) Xx)) (forall ((Xx tptp.a) (Xy tptp.a)) (=> (and (@ (@ tptp.cR Xx) Xy) (@ (@ tptp.cR Xy) Xx)) (= Xx Xy))) (forall ((Xx tptp.a) (Xy tptp.a)) (or (@ (@ tptp.cR Xx) Xy) (@ (@ tptp.cR Xy) Xx))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ (@ tptp.cR Xu) Xv) (@ tptp.cS Xv)) (@ tptp.cS Xu))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ (@ tptp.cR Xu) Xv) (@ tptp.cT Xv)) (@ tptp.cT Xu)))) (or (forall ((Xx tptp.a)) (=> (@ tptp.cS Xx) (@ tptp.cT Xx))) (forall ((Xx tptp.a)) (=> (@ tptp.cT Xx) (@ tptp.cS Xx)))))))
% 0.20/0.52 (set-info :filename cvc5---1.0.5_16470)
% 0.20/0.52 (check-sat-assuming ( true ))
% 0.20/0.52 ------- get file name : TPTP file name is SEV067^5
% 0.20/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16470.smt2...
% 0.20/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.52 % SZS status Theorem for SEV067^5
% 0.20/0.52 % SZS output start Proof for SEV067^5
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (forall ((Xx tptp.a) (Xy tptp.a)) (or (@ (@ tptp.cR Xx) Xy) (@ (@ tptp.cR Xy) Xx))))) (let ((_let_2 (forall ((Xx tptp.a)) (@ (@ tptp.cR Xx) Xx)))) (let ((_let_3 (not (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ tptp.cR Xx))) (=> (and (@ _let_1 Xy) (@ (@ tptp.cR Xy) Xz)) (@ _let_1 Xz)))) _let_2 (forall ((Xx tptp.a) (Xy tptp.a)) (=> (and (@ (@ tptp.cR Xx) Xy) (@ (@ tptp.cR Xy) Xx)) (= Xx Xy))) _let_1 (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ (@ tptp.cR Xu) Xv) (@ tptp.cS Xv)) (@ tptp.cS Xu))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ (@ tptp.cR Xu) Xv) (@ tptp.cT Xv)) (@ tptp.cT Xu)))) (or (forall ((Xx tptp.a)) (=> (@ tptp.cS Xx) (@ tptp.cT Xx))) (forall ((Xx tptp.a)) (=> (@ tptp.cT Xx) (@ tptp.cS Xx)))))))) (let ((_let_4 (forall ((Xx tptp.a) (Xy tptp.a)) (or (ho_3 (ho_6 k_5 Xx) Xy) (ho_3 (ho_6 k_5 Xy) Xx))))) (let ((_let_5 (ho_3 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_6 (ho_3 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_7 (or _let_6 _let_5))) (let ((_let_8 (0))) (let ((_let_9 (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_10 (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_11 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_12 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_13 (forall ((Xx tptp.a)) (or (not (ho_3 k_4 Xx)) (ho_3 k_2 Xx))))) (let ((_let_14 (forall ((Xx tptp.a)) (or (not (ho_3 k_2 Xx)) (ho_3 k_4 Xx))))) (let ((_let_15 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_3 (ho_6 k_5 Xu) Xv)) (not (ho_3 k_4 Xv)) (ho_3 k_4 Xu))))) (let ((_let_16 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_3 (ho_6 k_5 Xu) Xv)) (not (ho_3 k_2 Xv)) (ho_3 k_2 Xu))))) (let ((_let_17 (not (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_6 k_5 Xx))) (or (not (ho_3 _let_1 Xy)) (not (ho_3 (ho_6 k_5 Xy) Xz)) (ho_3 _let_1 Xz)))) (forall ((Xx tptp.a)) (ho_3 (ho_6 k_5 Xx) Xx)) (forall ((Xx tptp.a) (Xy tptp.a)) (or (not (ho_3 (ho_6 k_5 Xx) Xy)) (not (ho_3 (ho_6 k_5 Xy) Xx)) (= Xx Xy))) _let_4 _let_16 _let_15) (or _let_14 _let_13))))) (let ((_let_18 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ tptp.cR Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ tptp.cR Xy) Xz)) (@ _let_1 Xz)))) _let_2 (forall ((Xx tptp.a) (Xy tptp.a)) (or (not (@ (@ tptp.cR Xx) Xy)) (not (@ (@ tptp.cR Xy) Xx)) (= Xx Xy))) _let_1 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ (@ tptp.cR Xu) Xv)) (not (@ tptp.cS Xv)) (@ tptp.cS Xu))) (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ (@ tptp.cR Xu) Xv)) (not (@ tptp.cT Xv)) (@ tptp.cT Xu)))) (or (forall ((Xx tptp.a)) (or (not (@ tptp.cS Xx)) (@ tptp.cT Xx))) (forall ((Xx tptp.a)) (or (not (@ tptp.cT Xx)) (@ tptp.cS Xx)))))) _let_17))))) (PREPROCESS :args ((and _let_12 _let_11 _let_10 _let_9)))) :args ((and _let_17 _let_12 _let_11 _let_10 _let_9))) :args _let_8))) (let ((_let_19 (NOT_IMPLIES_ELIM1 _let_18))) (let ((_let_20 (not _let_7))) (let ((_let_21 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_22 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (not _let_22))) (let ((_let_24 (not _let_5))) (let ((_let_25 (or _let_24 _let_23 _let_21))) (let ((_let_26 (_let_16))) (let ((_let_27 (ho_3 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_21))) (let ((_let_30 (not _let_29))) (let ((_let_31 (NOT_IMPLIES_ELIM2 _let_18))) (let ((_let_32 (or))) (let ((_let_33 (not _let_13))) (let ((_let_34 (_let_33))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_34)) :args _let_34)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_13))) (REFL :args (_let_30)) :args _let_32)) (NOT_OR_ELIM _let_31 :args (1)) :args (_let_30 true _let_13)))) (let ((_let_36 (ho_3 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_37 (or _let_23 _let_36))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_14))) (let ((_let_40 (_let_39))) (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_39) _let_14))) (REFL :args (_let_38)) :args _let_32)) (NOT_OR_ELIM _let_31 :args _let_8) :args (_let_38 true _let_14)))) (let ((_let_42 (not _let_6))) (let ((_let_43 (or _let_42 _let_28 _let_36))) (let ((_let_44 (_let_15))) (let ((_let_45 (_let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_6 _let_5 _let_20))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_36 _let_28 _let_42 (not _let_43)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 1)) _let_41 :args ((not _let_36) true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG (REFL :args (_let_29)) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_32)) :args ((or _let_27 _let_29))) _let_35 :args (_let_27 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_ENUM)) :args _let_44)) (AND_ELIM _let_19 :args (5)) :args (_let_43 false _let_15)) :args (_let_42 true _let_36 false _let_27 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_23 _let_21 _let_24 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_32)) :args ((or _let_22 _let_37))) _let_41 :args (_let_22 true _let_37)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 1)) _let_35 :args ((not _let_21) true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_ENUM)) :args _let_26)) (AND_ELIM _let_19 :args (4)) :args (_let_25 false _let_16)) :args (_let_24 false _let_22 true _let_21 false _let_25)) :args (_let_20 true _let_6 true _let_5)) (AND_ELIM _let_19 :args (3)) :args (false true _let_7 false _let_4)) :args (_let_3 true))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.53 )
% 0.20/0.53 % SZS output end Proof for SEV067^5
% 0.20/0.53 % cvc5---1.0.5 exiting
% 0.20/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------