TSTP Solution File: SEV245^6 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV245^6 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 19:22:00 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
% 0.07/0.13 % Problem : SEV245^6 : TPTP v8.1.2. Released v5.1.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 03:21:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 % File : SEV245^6 : TPTP v8.1.2. Released v5.1.0.
% 0.20/0.53 % Domain : Set Theory
% 0.20/0.53 % Problem : TPS problem from BASIC-HO-THMS
% 0.20/0.53 % Version : Especial.
% 0.20/0.53 % English :
% 0.20/0.53
% 0.20/0.53 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.53 % Source : [Bro09]
% 0.20/0.53 % Names : tps_0957 [Bro09]
% 0.20/0.53 % : tps_0964 [Bro09]
% 0.20/0.53
% 0.20/0.53 % Status : Theorem
% 0.20/0.53 % Rating : 0.09 v8.1.0, 0.17 v7.5.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0
% 0.20/0.53 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.53 % Number of atoms : 5 ( 0 equ; 0 cnn)
% 0.20/0.53 % Maximal formula atoms : 5 ( 5 avg)
% 0.20/0.53 % Number of connectives : 25 ( 0 ~; 0 |; 2 &; 16 @)
% 0.20/0.53 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.53 % Maximal formula depth : 13 ( 13 avg)
% 0.20/0.53 % Number of types : 2 ( 1 usr)
% 0.20/0.53 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.53 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.20/0.53 % Number of variables : 10 ( 1 ^; 7 !; 2 ?; 10 :)
% 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 % : Renamed from SYO319^5
% 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(cK,type,
% 0.20/0.53 cK: ( a > $o ) > a > $o ).
% 0.20/0.53
% 0.20/0.53 thf(cTHM116_2S,conjecture,
% 0.20/0.53 ( ! [X: a > $o,Y: a > $o] :
% 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 ( ( cK @ X @ Xx )
% 0.20/0.53 => ( cK @ Y @ Xx ) ) )
% 0.20/0.53 => ! [Xx: a] :
% 0.20/0.53 ( ? [S: a > $o] :
% 0.20/0.53 ( ! [Xx0: a] :
% 0.20/0.53 ( ( S @ Xx0 )
% 0.20/0.53 => ( cK @ S @ Xx0 ) )
% 0.20/0.53 & ( S @ Xx ) )
% 0.20/0.53 => ( cK
% 0.20/0.53 @ ^ [Xx0: a] :
% 0.20/0.53 ? [S: a > $o] :
% 0.20/0.53 ( ! [Xx1: a] :
% 0.20/0.53 ( ( S @ Xx1 )
% 0.20/0.53 => ( cK @ S @ Xx1 ) )
% 0.20/0.53 & ( S @ Xx0 ) )
% 0.20/0.53 @ Xx ) ) ) ).
% 0.20/0.53
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.uGmaLzTQL2/cvc5---1.0.5_28930.p...
% 0.20/0.53 (declare-sort $$unsorted 0)
% 0.20/0.53 (declare-sort tptp.a 0)
% 0.20/0.53 (declare-fun tptp.cK ((-> tptp.a Bool) tptp.a) Bool)
% 0.20/0.53 (assert (not (=> (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (forall ((Xx tptp.a)) (=> (@ (@ tptp.cK X) Xx) (@ (@ tptp.cK Y) Xx))))) (forall ((Xx tptp.a)) (=> (exists ((S (-> tptp.a Bool))) (and (forall ((Xx0 tptp.a)) (=> (@ S Xx0) (@ (@ tptp.cK S) Xx0))) (@ S Xx))) (@ (@ tptp.cK (lambda ((Xx0 tptp.a)) (exists ((S (-> tptp.a Bool))) (and (forall ((Xx1 tptp.a)) (=> (@ S Xx1) (@ (@ tptp.cK S) Xx1))) (@ S Xx0))))) Xx))))))
% 0.20/0.53 (set-info :filename cvc5---1.0.5_28930)
% 0.20/0.53 (check-sat-assuming ( true ))
% 0.20/0.53 ------- get file name : TPTP file name is SEV245^6
% 0.20/0.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28930.smt2...
% 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for SEV245^6
% 0.20/0.53 % SZS output start Proof for SEV245^6
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (not (=> (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (forall ((Xx tptp.a)) (=> (@ (@ tptp.cK X) Xx) (@ (@ tptp.cK Y) Xx))))) (forall ((Xx tptp.a)) (=> (exists ((S (-> tptp.a Bool))) (and (forall ((Xx0 tptp.a)) (=> (@ S Xx0) (@ (@ tptp.cK S) Xx0))) (@ S Xx))) (@ (@ tptp.cK (lambda ((Xx0 tptp.a)) (exists ((S (-> tptp.a Bool))) (and (forall ((Xx1 tptp.a)) (=> (@ S Xx1) (@ (@ tptp.cK S) Xx1))) (@ S Xx0))))) Xx))))))) (let ((_let_2 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_3 (forall ((Xx1 tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx1)) (ho_4 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) Xx1))))) (let ((_let_4 (not _let_2))) (let ((_let_5 (not _let_3))) (let ((_let_6 (or _let_5 _let_4))) (let ((_let_7 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_8 (or _let_4 _let_7))) (let ((_let_9 (forall ((Xx tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx)) (ho_4 k_3 Xx))))) (let ((_let_10 (not _let_8))) (let ((_let_11 (ho_4 (ho_6 k_5 k_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_12 (ho_4 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_13 (not _let_12))) (let ((_let_14 (not _let_9))) (let ((_let_15 (or _let_14 _let_13 _let_11))) (let ((_let_16 (forall ((BOUND_VARIABLE_778 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_775 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_642 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (ho_4 BOUND_VARIABLE_778 Xx)) (ho_4 BOUND_VARIABLE_775 Xx)))) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_778) BOUND_VARIABLE_642)) (ho_4 (ho_6 k_5 BOUND_VARIABLE_775) BOUND_VARIABLE_642))))) (let ((_let_17 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_19 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_21 (forall ((BOUND_VARIABLE_721 tptp.a)) (= (ho_4 k_3 BOUND_VARIABLE_721) (not (forall ((BOUND_VARIABLE_740 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a)) (or (not (ho_4 BOUND_VARIABLE_740 Xx1)) (ho_4 (ho_6 k_5 BOUND_VARIABLE_740) Xx1)))) (not (ho_4 BOUND_VARIABLE_740 BOUND_VARIABLE_721))))))))) (let ((_let_22 (forall ((Xx tptp.a) (BOUND_VARIABLE_760 |u_(-> tptp.a Bool)|)) (or (ho_4 (ho_6 k_5 k_3) Xx) (not (forall ((Xx0 tptp.a)) (or (not (ho_4 BOUND_VARIABLE_760 Xx0)) (ho_4 (ho_6 k_5 BOUND_VARIABLE_760) Xx0)))) (not (ho_4 BOUND_VARIABLE_760 Xx)))))) (let ((_let_23 (not (=> _let_16 _let_22)))) (let ((_let_24 (forall ((BOUND_VARIABLE_721 tptp.a)) (= (not (forall ((S (-> tptp.a Bool))) (or (not (forall ((Xx1 tptp.a)) (or (not (@ S Xx1)) (@ (@ tptp.cK S) Xx1)))) (not (@ S BOUND_VARIABLE_721))))) (ll_2 BOUND_VARIABLE_721))))) (let ((_let_25 (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (BOUND_VARIABLE_642 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (not (@ (@ tptp.cK X) BOUND_VARIABLE_642)) (@ (@ tptp.cK Y) BOUND_VARIABLE_642))))) (let ((_let_26 (not (=> _let_25 (forall ((Xx tptp.a) (BOUND_VARIABLE_686 (-> tptp.a Bool))) (or (@ (@ tptp.cK ll_2) Xx) (not (forall ((Xx0 tptp.a)) (or (not (@ BOUND_VARIABLE_686 Xx0)) (@ (@ tptp.cK BOUND_VARIABLE_686) Xx0)))) (not (@ BOUND_VARIABLE_686 Xx)))))))) (let ((_let_27 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> _let_25 (forall ((Xx tptp.a) (BOUND_VARIABLE_686 (-> tptp.a Bool))) (or (@ (@ tptp.cK (lambda ((Xx0 tptp.a)) (not (forall ((S (-> tptp.a Bool))) (or (not (forall ((Xx1 tptp.a)) (or (not (@ S Xx1)) (@ (@ tptp.cK S) Xx1)))) (not (@ S Xx0))))))) Xx) (not (forall ((Xx0 tptp.a)) (or (not (@ BOUND_VARIABLE_686 Xx0)) (@ (@ tptp.cK BOUND_VARIABLE_686) Xx0)))) (not (@ BOUND_VARIABLE_686 Xx)))))) _let_26))))) (PREPROCESS :args (_let_24))) (PREPROCESS :args ((= (and _let_26 _let_24) (and _let_23 _let_21))))) (PREPROCESS :args ((and _let_20 _let_19 _let_18 _let_17)))) :args ((and _let_23 _let_21 _let_20 _let_19 _let_18 _let_17))))) (let ((_let_28 (AND_ELIM _let_27 :args (0)))) (let ((_let_29 (_let_16))) (let ((_let_30 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_12))) (let ((_let_33 (forall ((Xx0 tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0)) (ho_4 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) Xx0))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_11 _let_34 _let_31))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or))) (let ((_let_38 (not _let_22))) (let ((_let_39 (_let_38))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_39)) :args _let_39)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_22))) (REFL :args (_let_36)) :args _let_37)) (NOT_IMPLIES_ELIM2 _let_28) :args (_let_36 true _let_22)))) (let ((_let_41 (REFL :args (_let_35)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 1)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_37)) :args ((or _let_33 _let_35))) _let_40 :args (_let_33 true _let_35)))) (let ((_let_43 (_let_33))) (let ((_let_44 (_let_14))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_44)) :args _let_44)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_9))) (REFL :args (_let_10)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_11 _let_13 _let_14 (not _let_15)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 0)) _let_40 :args ((not _let_11) true _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_12 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 2)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_37)) :args ((or _let_30 _let_35))) _let_40 :args (_let_30 true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_43) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) false))))) :args _let_43)) _let_42 :args (_let_32 false _let_33)) :args (_let_12 false _let_30 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_6 k_5 BOUND_VARIABLE_778) BOUND_VARIABLE_642) false)) (ho_6 k_5 BOUND_VARIABLE_775)))) :args _let_29)) (NOT_IMPLIES_ELIM1 _let_28) :args (_let_15 false _let_16)) :args (_let_14 true _let_11 false _let_12 false _let_15)) :args (_let_10 true _let_9)))) (let ((_let_46 (forall ((BOUND_VARIABLE_740 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a)) (or (not (ho_4 BOUND_VARIABLE_740 Xx1)) (ho_4 (ho_6 k_5 BOUND_VARIABLE_740) Xx1)))) (not (ho_4 BOUND_VARIABLE_740 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (= _let_7 _let_47))) (let ((_let_49 (_let_21))) (let ((_let_50 (not _let_48))) (let ((_let_51 (_let_46))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_4 _let_5 (not _let_6)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_51) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_4 BOUND_VARIABLE_740 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) false))))) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_48)) (CONG (REFL :args (_let_50)) (REFL :args (_let_7)) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_37)) :args ((or _let_7 _let_46 _let_50))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_8 1)) _let_45 :args ((not _let_7) true _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_49) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_4 k_3 BOUND_VARIABLE_721)))) :args _let_49)) (AND_ELIM _let_27 :args (1)) :args (_let_48 false _let_21)) :args (_let_46 true _let_7 false _let_48)) :args (_let_6 false _let_46)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_33 (= Xx0 Xx1)))) _let_42 :args (_let_3 false _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_8 0)) (CONG (REFL :args (_let_8)) (MACRO_SR_PRED_INTRO :args ((= (not _let_4) _let_2))) :args _let_37)) :args ((or _let_2 _let_8))) _let_45 :args (_let_2 true _let_8)) :args (false false _let_6 false _let_3 false _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.54 )
% 0.20/0.54 % SZS output end Proof for SEV245^6
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------