TSTP Solution File: SEV398^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV398^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 19:22:24 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 : SEV398^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 04:01:11 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : SEV398^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.53 % Domain : Set Theory
% 0.21/0.53 % Problem : TPS problem THM67A
% 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_0437 [Bro09]
% 0.21/0.53 % : THM67A [TPS]
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.21/0.53 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.21/0.53 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 10 ( 10 avg)
% 0.21/0.53 % Number of connectives : 29 ( 0 ~; 0 |; 2 &; 20 @)
% 0.21/0.53 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 10 ( 10 avg)
% 0.21/0.53 % Number of types : 2 ( 1 usr)
% 0.21/0.53 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.21/0.53 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.21/0.53 % SPC : TH0_THM_NEQ_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(a_type,type,
% 0.21/0.53 a: $tType ).
% 0.21/0.53
% 0.21/0.53 thf(cF,type,
% 0.21/0.53 cF: ( a > $o ) > a > $o ).
% 0.21/0.53
% 0.21/0.53 thf(cG,type,
% 0.21/0.53 cG: ( a > $o ) > a > $o ).
% 0.21/0.53
% 0.21/0.53 thf(cTHM67A_pme,conjecture,
% 0.21/0.53 ( ( ! [S: a > $o,T: a > $o] :
% 0.21/0.53 ( ! [Xx: a] :
% 0.21/0.53 ( ( S @ Xx )
% 0.21/0.53 => ( T @ Xx ) )
% 0.21/0.53 => ! [Xx: a] :
% 0.21/0.53 ( ( cF @ T @ Xx )
% 0.21/0.53 => ( cF @ S @ Xx ) ) )
% 0.21/0.53 & ! [S: a > $o] :
% 0.21/0.53 ( ! [Xx: a] :
% 0.21/0.53 ( ( S @ Xx )
% 0.21/0.53 => ( cF @ ( cG @ S ) @ Xx ) )
% 0.21/0.53 & ! [Xx: a] :
% 0.21/0.53 ( ( S @ Xx )
% 0.21/0.53 => ( cG @ ( cF @ S ) @ Xx ) ) ) )
% 0.21/0.53 => ! [S: a > $o,Xx: a] :
% 0.21/0.53 ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
% 0.21/0.53 <=> ( cF @ S @ Xx ) ) ) ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.reMvtcleGX/cvc5---1.0.5_9786.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-sort tptp.a 0)
% 0.21/0.53 (declare-fun tptp.cF ((-> tptp.a Bool) tptp.a) Bool)
% 0.21/0.53 (declare-fun tptp.cG ((-> tptp.a Bool) tptp.a) Bool)
% 0.21/0.53 (assert (not (=> (and (forall ((S (-> tptp.a Bool)) (T (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ S Xx) (@ T Xx))) (forall ((Xx tptp.a)) (=> (@ (@ tptp.cF T) Xx) (@ (@ tptp.cF S) Xx))))) (forall ((S (-> tptp.a Bool))) (and (forall ((Xx tptp.a)) (=> (@ S Xx) (@ (@ tptp.cF (@ tptp.cG S)) Xx))) (forall ((Xx tptp.a)) (=> (@ S Xx) (@ (@ tptp.cG (@ tptp.cF S)) Xx)))))) (forall ((S (-> tptp.a Bool)) (Xx tptp.a)) (let ((_let_1 (@ tptp.cF S))) (= (@ (@ tptp.cF (@ tptp.cG _let_1)) Xx) (@ _let_1 Xx)))))))
% 0.21/0.53 (set-info :filename cvc5---1.0.5_9786)
% 0.21/0.53 (check-sat-assuming ( true ))
% 0.21/0.53 ------- get file name : TPTP file name is SEV398^5
% 0.21/0.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9786.smt2...
% 0.21/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for SEV398^5
% 0.21/0.53 % SZS output start Proof for SEV398^5
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (forall ((S (-> tptp.a Bool)) (Xx tptp.a)) (let ((_let_1 (@ tptp.cF S))) (= (@ (@ tptp.cF (@ tptp.cG _let_1)) Xx) (@ _let_1 Xx)))))) (let ((_let_2 (not (=> (and (forall ((S (-> tptp.a Bool)) (T (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ S Xx) (@ T Xx))) (forall ((Xx tptp.a)) (=> (@ (@ tptp.cF T) Xx) (@ (@ tptp.cF S) Xx))))) (forall ((S (-> tptp.a Bool))) (and (forall ((Xx tptp.a)) (=> (@ S Xx) (@ (@ tptp.cF (@ tptp.cG S)) Xx))) (forall ((Xx tptp.a)) (=> (@ S Xx) (@ (@ tptp.cG (@ tptp.cF S)) Xx)))))) _let_1)))) (let ((_let_3 (forall ((BOUND_VARIABLE_714 |u_(-> tptp.a Bool)|) (Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_714 Xx)) (ho_2 (ho_4 k_5 (ho_4 k_3 BOUND_VARIABLE_714)) Xx))))) (let ((_let_4 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_5 (ho_4 k_5 _let_4))) (let ((_let_6 (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (ho_2 _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_7 (0))) (let ((_let_8 (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_9 (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_10 (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_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_11 (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_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_12 (forall ((BOUND_VARIABLE_698 |u_(-> tptp.a Bool)|) (Xx tptp.a)) (let ((_let_1 (ho_4 k_3 BOUND_VARIABLE_698))) (= (ho_2 _let_1 Xx) (ho_2 (ho_4 k_3 (ho_4 k_5 _let_1)) Xx)))))) (let ((_let_13 (forall ((BOUND_VARIABLE_723 |u_(-> tptp.a Bool)|) (Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_723 Xx)) (ho_2 (ho_4 k_3 (ho_4 k_5 BOUND_VARIABLE_723)) Xx))))) (let ((_let_14 (forall ((BOUND_VARIABLE_732 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_735 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_641 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_732 Xx)) (ho_2 BOUND_VARIABLE_735 Xx)))) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_735) BOUND_VARIABLE_641)) (ho_2 (ho_4 k_3 BOUND_VARIABLE_732) BOUND_VARIABLE_641))))) (let ((_let_15 (not (=> (and _let_14 _let_13 _let_3) _let_12)))) (let ((_let_16 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (and (forall ((S (-> tptp.a Bool)) (T (-> tptp.a Bool)) (BOUND_VARIABLE_641 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (@ S Xx)) (@ T Xx)))) (not (@ (@ tptp.cF T) BOUND_VARIABLE_641)) (@ (@ tptp.cF S) BOUND_VARIABLE_641))) (forall ((BOUND_VARIABLE_660 (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ BOUND_VARIABLE_660 Xx)) (@ (@ tptp.cF (@ tptp.cG BOUND_VARIABLE_660)) Xx))) (forall ((BOUND_VARIABLE_671 (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ BOUND_VARIABLE_671 Xx)) (@ (@ tptp.cG (@ tptp.cF BOUND_VARIABLE_671)) Xx)))) _let_1)) _let_15))))) (PREPROCESS :args ((and _let_11 _let_10 _let_9 _let_8)))) :args ((and _let_15 _let_11 _let_10 _let_9 _let_8))) :args _let_7))) (let ((_let_17 (NOT_IMPLIES_ELIM1 _let_16))) (let ((_let_18 (forall ((Xx tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Xx)) (ho_2 (ho_4 k_5 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) Xx))))) (let ((_let_19 (not _let_6))) (let ((_let_20 (ho_2 _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_21 (ho_2 (ho_4 k_3 _let_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not _let_18))) (let ((_let_24 (or _let_23 _let_22 _let_20))) (let ((_let_25 (_let_14))) (let ((_let_26 (= _let_20 _let_21))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or))) (let ((_let_29 (not _let_12))) (let ((_let_30 (_let_29))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_30)) :args _let_30)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_12))) (REFL :args (_let_27)) :args _let_28)) (NOT_IMPLIES_ELIM2 _let_16) :args (_let_27 true _let_12)))) (let ((_let_32 (not _let_20))) (let ((_let_33 (or _let_32 _let_21))) (let ((_let_34 (_let_26))) (let ((_let_35 (_let_13))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_21 _let_32 (not _let_33)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_35) :args (_let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) (AND_ELIM _let_17 :args (1)) :args (_let_33 false _let_13)) (CNF_EQUIV_NEG2 :args _let_34) _let_31 :args (_let_32 false _let_33 true _let_21 true _let_26)))) (let ((_let_37 (_let_23))) (let ((_let_38 (_let_3))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_38)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_37)) :args _let_37)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_18))) (REFL :args (_let_19)) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_20 _let_22 _let_23 (not _let_24)))) _let_36 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_34) :args ((or _let_20 _let_21 _let_26))) _let_36 _let_31 :args (_let_21 true _let_20 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_25) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_2 (ho_4 k_3 BOUND_VARIABLE_735) BOUND_VARIABLE_641) false)) (ho_4 k_3 BOUND_VARIABLE_732)))) :args _let_25)) (AND_ELIM _let_17 :args _let_7) :args (_let_24 false _let_14)) :args (_let_23 true _let_20 false _let_21 false _let_24)) :args (_let_19 true _let_18)) (AND_ELIM _let_17 :args (2)) :args (false true _let_6 false _let_3)) :args (_let_2 true)))))))))))))))))))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for SEV398^5
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------