TSTP Solution File: SEV185^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV185^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 19:21:48 EDT 2023
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV185^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : do_cvc5 %s %d
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Thu Aug 24 03:04:26 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.13/0.38 %----Proving TH0
% 0.13/0.40 %------------------------------------------------------------------------------
% 0.13/0.40 % File : SEV185^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.40 % Domain : Set Theory (Sets of sets)
% 0.13/0.40 % Problem : TPS problem THM564
% 0.13/0.40 % Version : Especial.
% 0.13/0.40 % English :
% 0.13/0.40
% 0.13/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.13/0.40 % Source : [Bro09]
% 0.13/0.40 % Names : tps_0453 [Bro09]
% 0.13/0.40 % : THM564 [TPS]
% 0.13/0.40
% 0.13/0.40 % Status : Theorem
% 0.13/0.40 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 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
% 0.13/0.40 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.13/0.40 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.13/0.40 % Maximal formula atoms : 0 ( 0 avg)
% 0.13/0.40 % Number of connectives : 23 ( 0 ~; 0 |; 2 &; 13 @)
% 0.13/0.40 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.13/0.40 % Maximal formula depth : 13 ( 13 avg)
% 0.13/0.40 % Number of types : 2 ( 1 usr)
% 0.13/0.40 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.13/0.40 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.13/0.40 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.13/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.13/0.40
% 0.13/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.13/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.13/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.13/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.13/0.40 % : Polymorphic definitions expanded.
% 0.13/0.40 %------------------------------------------------------------------------------
% 0.13/0.40 thf(b_type,type,
% 0.13/0.40 b: $tType ).
% 0.13/0.40
% 0.13/0.40 thf(cTHM564_pme,conjecture,
% 0.13/0.40 ! [P: ( b > $o ) > b > $o,S: ( b > $o ) > $o] :
% 0.13/0.40 ( ! [Xx: b > $o] :
% 0.13/0.40 ( ( S @ Xx )
% 0.13/0.40 => ! [X: b > $o,Xy: b] :
% 0.13/0.40 ( ( ! [Xx0: b] :
% 0.13/0.40 ( ( X @ Xx0 )
% 0.13/0.40 => ( Xx @ Xx0 ) )
% 0.13/0.40 & ( P @ X @ Xy ) )
% 0.13/0.40 => ( Xx @ Xy ) ) )
% 0.13/0.40 => ! [X: b > $o,Xy: b] :
% 0.13/0.40 ( ( ! [Xx: b] :
% 0.13/0.40 ( ( X @ Xx )
% 0.13/0.40 => ! [S0: b > $o] :
% 0.13/0.40 ( ( S @ S0 )
% 0.13/0.40 => ( S0 @ Xx ) ) )
% 0.13/0.40 & ( P @ X @ Xy ) )
% 0.13/0.40 => ! [S0: b > $o] :
% 0.13/0.40 ( ( S @ S0 )
% 0.13/0.40 => ( S0 @ Xy ) ) ) ) ).
% 0.13/0.40
% 0.13/0.40 %------------------------------------------------------------------------------
% 0.13/0.40 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wj0FsM47eq/cvc5---1.0.5_8046.p...
% 0.13/0.40 (declare-sort $$unsorted 0)
% 0.13/0.40 (declare-sort tptp.b 0)
% 0.13/0.40 (assert (not (forall ((P (-> (-> tptp.b Bool) tptp.b Bool)) (S (-> (-> tptp.b Bool) Bool))) (=> (forall ((Xx (-> tptp.b Bool))) (=> (@ S Xx) (forall ((X (-> tptp.b Bool)) (Xy tptp.b)) (=> (and (forall ((Xx0 tptp.b)) (=> (@ X Xx0) (@ Xx Xx0))) (@ (@ P X) Xy)) (@ Xx Xy))))) (forall ((X (-> tptp.b Bool)) (Xy tptp.b)) (=> (and (forall ((Xx tptp.b)) (=> (@ X Xx) (forall ((S0 (-> tptp.b Bool))) (=> (@ S S0) (@ S0 Xx))))) (@ (@ P X) Xy)) (forall ((S0 (-> tptp.b Bool))) (=> (@ S S0) (@ S0 Xy)))))))))
% 0.13/0.40 (set-info :filename cvc5---1.0.5_8046)
% 0.13/0.40 (check-sat-assuming ( true ))
% 0.13/0.40 ------- get file name : TPTP file name is SEV185^5
% 0.13/0.40 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8046.smt2...
% 0.13/0.40 --- Run --ho-elim --full-saturate-quant at 10...
% 0.13/0.40 % SZS status Theorem for SEV185^5
% 0.13/0.40 % SZS output start Proof for SEV185^5
% 0.13/0.40 (
% 0.13/0.40 (let ((_let_1 (not (forall ((P (-> (-> tptp.b Bool) tptp.b Bool)) (S (-> (-> tptp.b Bool) Bool))) (=> (forall ((Xx (-> tptp.b Bool))) (=> (@ S Xx) (forall ((X (-> tptp.b Bool)) (Xy tptp.b)) (=> (and (forall ((Xx0 tptp.b)) (=> (@ X Xx0) (@ Xx Xx0))) (@ (@ P X) Xy)) (@ Xx Xy))))) (forall ((X (-> tptp.b Bool)) (Xy tptp.b)) (=> (and (forall ((Xx tptp.b)) (=> (@ X Xx) (forall ((S0 (-> tptp.b Bool))) (=> (@ S S0) (@ S0 Xx))))) (@ (@ P X) Xy)) (forall ((S0 (-> tptp.b Bool))) (=> (@ S S0) (@ S0 Xy)))))))))) (let ((_let_2 (forall ((Xx tptp.b) (BOUND_VARIABLE_755 |u_(-> tptp.b Bool)|)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Xx)) (not (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 BOUND_VARIABLE_755)) (ho_2 BOUND_VARIABLE_755 Xx))))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_5 (not _let_4))) (let ((_let_6 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_7 (not _let_6))) (let ((_let_8 (or _let_7 _let_5 _let_3))) (let ((_let_9 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_10 (ho_2 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_11 (not _let_10))) (let ((_let_12 (not _let_2))) (let ((_let_13 (forall ((BOUND_VARIABLE_765 |u_(-> tptp.b Bool)|) (BOUND_VARIABLE_647 tptp.b) (BOUND_VARIABLE_767 |u_(-> tptp.b Bool)|)) (or (not (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 BOUND_VARIABLE_765)) (not (forall ((Xx0 tptp.b)) (or (not (ho_2 BOUND_VARIABLE_767 Xx0)) (ho_2 BOUND_VARIABLE_765 Xx0)))) (not (ho_2 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_767) BOUND_VARIABLE_647)) (ho_2 BOUND_VARIABLE_765 BOUND_VARIABLE_647))))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_11 _let_5 _let_9))) (let ((_let_16 (forall ((BOUND_VARIABLE_749 |u_(-> _u_(-> tptp.b Bool)_ tptp.b Bool)|) (BOUND_VARIABLE_742 |u_(-> _u_(-> tptp.b Bool)_ Bool)|) (BOUND_VARIABLE_736 |u_(-> tptp.b Bool)|) (BOUND_VARIABLE_713 tptp.b) (BOUND_VARIABLE_747 |u_(-> tptp.b Bool)|)) (or (not (forall ((BOUND_VARIABLE_765 |u_(-> tptp.b Bool)|) (BOUND_VARIABLE_647 tptp.b) (BOUND_VARIABLE_767 |u_(-> tptp.b Bool)|)) (or (not (ho_3 BOUND_VARIABLE_742 BOUND_VARIABLE_765)) (not (forall ((Xx0 tptp.b)) (or (not (ho_2 BOUND_VARIABLE_767 Xx0)) (ho_2 BOUND_VARIABLE_765 Xx0)))) (not (ho_2 (ho_4 BOUND_VARIABLE_749 BOUND_VARIABLE_767) BOUND_VARIABLE_647)) (ho_2 BOUND_VARIABLE_765 BOUND_VARIABLE_647)))) (not (forall ((Xx tptp.b) (BOUND_VARIABLE_755 |u_(-> tptp.b Bool)|)) (or (not (ho_2 BOUND_VARIABLE_747 Xx)) (not (ho_3 BOUND_VARIABLE_742 BOUND_VARIABLE_755)) (ho_2 BOUND_VARIABLE_755 Xx)))) (not (ho_2 (ho_4 BOUND_VARIABLE_749 BOUND_VARIABLE_747) BOUND_VARIABLE_713)) (not (ho_3 BOUND_VARIABLE_742 BOUND_VARIABLE_736)) (ho_2 BOUND_VARIABLE_736 BOUND_VARIABLE_713))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (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_19 (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_20 (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_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_21 (forall ((x |u_(-> _u_(-> tptp.b Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.b Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.b Bool)|)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_22 (forall ((u |u_(-> _u_(-> tptp.b Bool)_ tptp.b Bool)|) (e |u_(-> tptp.b Bool)|) (i |u_(-> tptp.b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.b Bool)_ tptp.b Bool)|)) (not (forall ((ii |u_(-> tptp.b Bool)|)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_23 (forall ((x |u_(-> _u_(-> tptp.b Bool)_ tptp.b Bool)|) (y |u_(-> _u_(-> tptp.b Bool)_ tptp.b Bool)|)) (or (not (forall ((z |u_(-> tptp.b Bool)|)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_24 (not _let_16))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((P (-> (-> tptp.b Bool) tptp.b Bool)) (S (-> (-> tptp.b Bool) Bool)) (BOUND_VARIABLE_715 (-> tptp.b Bool)) (BOUND_VARIABLE_713 tptp.b) (BOUND_VARIABLE_711 (-> tptp.b Bool))) (or (not (forall ((Xx (-> tptp.b Bool)) (BOUND_VARIABLE_647 tptp.b) (BOUND_VARIABLE_645 (-> tptp.b Bool))) (or (not (@ S Xx)) (not (forall ((Xx0 tptp.b)) (or (not (@ BOUND_VARIABLE_645 Xx0)) (@ Xx Xx0)))) (not (@ (@ P BOUND_VARIABLE_645) BOUND_VARIABLE_647)) (@ Xx BOUND_VARIABLE_647)))) (not (forall ((Xx tptp.b) (BOUND_VARIABLE_672 (-> tptp.b Bool))) (or (not (@ BOUND_VARIABLE_711 Xx)) (not (@ S BOUND_VARIABLE_672)) (@ BOUND_VARIABLE_672 Xx)))) (not (@ (@ P BOUND_VARIABLE_711) BOUND_VARIABLE_713)) (not (@ S BOUND_VARIABLE_715)) (@ BOUND_VARIABLE_715 BOUND_VARIABLE_713)))) _let_24))))))) (let ((_let_26 (or))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_24))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_16))) (REFL :args (_let_17)) :args _let_26)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_25 (PREPROCESS :args ((and _let_23 _let_22 _let_21 _let_20 _let_19 _let_18)))) :args ((and _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18))) :args (0)) :args (_let_17 true _let_16)))) (let ((_let_28 (REFL :args (_let_15)))) (let ((_let_29 (not _let_8))) (let ((_let_30 (or _let_7 _let_3))) (let ((_let_31 (forall ((Xx0 tptp.b)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Xx0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx0))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (not _let_31))) (let ((_let_34 (or _let_5 _let_33 _let_11 _let_9))) (let ((_let_35 (_let_13))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 3)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_26)) :args ((or _let_4 _let_15))) _let_27 :args (_let_4 true _let_15)))) (let ((_let_37 (_let_33))) (let ((_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_33) _let_31))) (REFL :args (_let_32)) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_11 _let_5 _let_9 _let_33 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 2)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_26)) :args ((or _let_10 _let_15))) _let_27 :args (_let_10 true _let_15)) _let_36 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_15 4)) _let_27 :args ((not _let_9) true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_35) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 BOUND_VARIABLE_765) false)) (not (= (ho_2 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_767) BOUND_VARIABLE_647) false))))) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 0)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_26)) :args ((or _let_13 _let_15))) _let_27 :args (_let_13 true _let_15)) :args (_let_34 false _let_13)) :args (_let_33 false _let_10 false _let_4 true _let_9 false _let_34)) :args (_let_32 true _let_31)))) (let ((_let_39 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_5 _let_7 _let_3 _let_29))) _let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_26)) :args ((or _let_6 _let_30))) _let_38 :args (_let_6 true _let_30)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 1)) _let_38 :args ((not _let_3) true _let_30)) :args (_let_29 false _let_4 false _let_6 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 1)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_2))) :args _let_26)) :args ((or _let_2 _let_15))) _let_27 :args (_let_2 true _let_15)) :args (false true _let_8 false _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))
% 0.13/0.41 )
% 0.13/0.41 % SZS output end Proof for SEV185^5
% 0.13/0.41 % cvc5---1.0.5 exiting
% 0.13/0.41 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------