TSTP Solution File: SEV121^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV121^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 19:21:36 EDT 2023
% Result : Theorem 0.22s 0.75s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV121^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.18/0.37 % Computer : n012.cluster.edu
% 0.18/0.37 % Model : x86_64 x86_64
% 0.18/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37 % Memory : 8042.1875MB
% 0.18/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37 % CPULimit : 300
% 0.18/0.37 % WCLimit : 300
% 0.18/0.37 % DateTime : Thu Aug 24 01:57:27 EDT 2023
% 0.18/0.37 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.75 %------------------------------------------------------------------------------
% 0.22/0.75 % File : SEV121^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.75 % Domain : Set Theory (Relations)
% 0.22/0.75 % Problem : TPS problem THM47C
% 0.22/0.75 % Version : Especial.
% 0.22/0.75 % English :
% 0.22/0.75
% 0.22/0.75 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.75 % Source : [Bro09]
% 0.22/0.75 % Names : tps_0445 [Bro09]
% 0.22/0.75 % : THM47C [TPS]
% 0.22/0.75 % : tps_0444 [Bro09]
% 0.22/0.75 % : X5303 [TPS]
% 0.22/0.75
% 0.22/0.75 % Status : Theorem
% 0.22/0.75 % Rating : 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.22/0.75 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.22/0.75 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.22/0.75 % Maximal formula atoms : 1 ( 2 avg)
% 0.22/0.75 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.22/0.75 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.22/0.75 % Maximal formula depth : 1 ( 1 avg)
% 0.22/0.75 % Number of types : 2 ( 0 usr)
% 0.22/0.75 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.22/0.75 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.22/0.75 % Number of variables : 6 ( 4 ^; 2 !; 0 ?; 6 :)
% 0.22/0.75 % SPC : TH0_THM_EQU_NAR
% 0.22/0.75
% 0.22/0.75 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.75 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.75 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.75 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.75 % : Polymorphic definitions expanded.
% 0.22/0.75 %------------------------------------------------------------------------------
% 0.22/0.75 thf(cTHM47C_pme,conjecture,
% 0.22/0.75 ( ( ^ [Xu: $i,Xv: $i] : ( Xu = Xv ) )
% 0.22/0.75 = ( ^ [Xx: $i,Xy: $i] :
% 0.22/0.75 ! [Xp: $i > $i > $o] :
% 0.22/0.75 ( ! [Xx0: $i] : ( Xp @ Xx0 @ Xx0 )
% 0.22/0.75 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 0.22/0.75
% 0.22/0.75 %------------------------------------------------------------------------------
% 0.22/0.75 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.HS9WFLLdrZ/cvc5---1.0.5_31173.p...
% 0.22/0.75 (declare-sort $$unsorted 0)
% 0.22/0.75 (assert (not (= (lambda ((Xu $$unsorted) (Xv $$unsorted)) (= Xu Xv)) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (forall ((Xp (-> $$unsorted $$unsorted Bool))) (=> (forall ((Xx0 $$unsorted)) (@ (@ Xp Xx0) Xx0)) (@ (@ Xp Xx) Xy)))))))
% 0.22/0.75 (set-info :filename cvc5---1.0.5_31173)
% 0.22/0.75 (check-sat-assuming ( true ))
% 0.22/0.75 ------- get file name : TPTP file name is SEV121^5
% 0.22/0.75 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31173.smt2...
% 0.22/0.75 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.75 % SZS status Theorem for SEV121^5
% 0.22/0.75 % SZS output start Proof for SEV121^5
% 0.22/0.75 (
% 0.22/0.75 (let ((_let_1 (lambda ((Xu $$unsorted) (Xv $$unsorted)) (= Xu Xv)))) (let ((_let_2 (not (= _let_1 (lambda ((Xx $$unsorted) (Xy $$unsorted)) (forall ((Xp (-> $$unsorted $$unsorted Bool))) (=> (forall ((Xx0 $$unsorted)) (@ (@ Xp Xx0) Xx0)) (@ (@ Xp Xx) Xy)))))))) (let ((_let_3 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_235))) (let ((_let_4 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_245 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_5 (ho_6 _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_235))) (let ((_let_6 (ho_6 _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_8 (ho_6 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_235))) (let ((_let_9 (= _let_8 _let_3))) (let ((_let_10 (forall ((BOUND_VARIABLE_626 $$unsorted) (BOUND_VARIABLE_627 $$unsorted)) (= (= BOUND_VARIABLE_626 BOUND_VARIABLE_627) (ho_6 (ho_5 k_4 BOUND_VARIABLE_626) BOUND_VARIABLE_627))))) (let ((_let_11 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_12 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_13 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_14 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_15 (forall ((BOUND_VARIABLE_616 $$unsorted) (BOUND_VARIABLE_617 $$unsorted)) (= (ho_6 (ho_5 k_7 BOUND_VARIABLE_616) BOUND_VARIABLE_617) (forall ((BOUND_VARIABLE_659 |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((Xx0 $$unsorted)) (ho_6 (ho_5 BOUND_VARIABLE_659 Xx0) Xx0))) (ho_6 (ho_5 BOUND_VARIABLE_659 BOUND_VARIABLE_616) BOUND_VARIABLE_617))))))) (let ((_let_16 (= k_4 k_7))) (let ((_let_17 (not _let_16))) (let ((_let_18 (forall ((BOUND_VARIABLE_626 $$unsorted) (BOUND_VARIABLE_627 $$unsorted)) (= (= BOUND_VARIABLE_626 BOUND_VARIABLE_627) (ll_3 BOUND_VARIABLE_626 BOUND_VARIABLE_627))))) (let ((_let_19 (forall ((BOUND_VARIABLE_616 $$unsorted) (BOUND_VARIABLE_617 $$unsorted)) (= (forall ((Xp (-> $$unsorted $$unsorted Bool))) (or (not (forall ((Xx0 $$unsorted)) (@ (@ Xp Xx0) Xx0))) (@ (@ Xp BOUND_VARIABLE_616) BOUND_VARIABLE_617))) (ll_2 BOUND_VARIABLE_616 BOUND_VARIABLE_617))))) (let ((_let_20 (not (= ll_2 ll_3)))) (let ((_let_21 (and _let_20 _let_19 _let_18))) (let ((_let_22 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (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 (= _let_1 (lambda ((Xx $$unsorted) (Xy $$unsorted)) (forall ((Xp (-> $$unsorted $$unsorted Bool))) (or (not (forall ((Xx0 $$unsorted)) (@ (@ Xp Xx0) Xx0))) (@ (@ Xp Xx) Xy)))))) _let_20))))) (PREPROCESS :args ((and _let_19 _let_18)))) :args (_let_21)) (PREPROCESS :args ((= _let_21 (and _let_17 _let_15 _let_10))))) (PREPROCESS :args ((and _let_14 _let_13 _let_12 _let_11)))) :args ((and _let_17 _let_15 _let_10 _let_14 _let_13 _let_12 _let_11))))) (let ((_let_23 (AND_ELIM _let_22 :args (2)))) (let ((_let_24 (_let_10))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (ho_5 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_27 (ho_6 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_235))) (let ((_let_28 (= _let_8 _let_27))) (let ((_let_29 (forall ((Xx0 $$unsorted)) (ho_6 (ho_5 k_4 Xx0) Xx0)))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_8))) (let ((_let_32 (forall ((BOUND_VARIABLE_659 |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((Xx0 $$unsorted)) (ho_6 (ho_5 BOUND_VARIABLE_659 Xx0) Xx0))) (ho_6 (ho_5 BOUND_VARIABLE_659 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_235))))) (let ((_let_33 (= _let_27 _let_32))) (let ((_let_34 (forall ((z $$unsorted)) (= (ho_6 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) z) (ho_6 (ho_5 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) z))))) (let ((_let_35 (not _let_28))) (let ((_let_36 (= _let_26 _let_7))) (let ((_let_37 (not _let_34))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (_let_12))) (let ((_let_40 (forall ((z $$unsorted)) (= (ho_5 k_7 z) (ho_5 k_4 z))))) (let ((_let_41 (not _let_36))) (let ((_let_42 (not _let_40))) (let ((_let_43 (or _let_42 _let_16))) (let ((_let_44 (_let_14))) (let ((_let_45 (or))) (let ((_let_46 (_let_42))) (let ((_let_47 (_let_37))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_47)) :args _let_47)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_34))) (REFL :args (_let_35)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_36 _let_37 (not _let_38)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_40))) (REFL :args (_let_41)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_16 _let_42 (not _let_43)))) (AND_ELIM _let_22 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (k_7 k_4 QUANTIFIERS_INST_ENUM)) :args _let_44))) (AND_ELIM _let_22 :args (3)) :args (_let_43 false _let_14)) :args (_let_42 true _let_16 false _let_43)) :args (_let_41 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (_let_7 _let_26 QUANTIFIERS_INST_ENUM)) :args _let_39))) (AND_ELIM _let_22 :args (5)) :args (_let_38 false _let_12)) :args (_let_37 true _let_36 false _let_38)) :args (_let_35 true _let_34)))) (let ((_let_49 (_let_28))) (let ((_let_50 (ho_6 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45))) (let ((_let_51 (_let_30))) (let ((_let_52 (_let_15))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_52) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_235 QUANTIFIERS_INST_E_MATCHING ((ho_6 (ho_5 k_7 BOUND_VARIABLE_616) BOUND_VARIABLE_617)))) :args _let_52)) (AND_ELIM _let_22 :args (1)) :args (_let_33 false _let_15)))) (let ((_let_54 (not _let_33))) (let ((_let_55 (not _let_27))) (let ((_let_56 (_let_33))) (let ((_let_57 (_let_32))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (k_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 BOUND_VARIABLE_659 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)))) :args _let_57)) (REORDERING (CNF_EQUIV_POS1 :args _let_56) :args ((or _let_55 _let_32 _let_54))) _let_53 (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_8 (not _let_31)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_51)) :args _let_51)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) (REFL :args ((not _let_50))) :args _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_24))) _let_23 :args (_let_50 false _let_10)) :args (_let_29 false _let_50)) (REORDERING (CNF_EQUIV_NEG1 :args _let_49) :args ((or _let_8 _let_27 _let_28))) _let_48 :args (_let_8 false _let_32 false _let_33 true _let_31 false _let_29 false _let_27 true _let_28)))) (let ((_let_59 (forall ((Xx0 $$unsorted)) (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_245 Xx0) Xx0)))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_5))) (let ((_let_62 (not _let_5))) (let ((_let_63 (not _let_61))) (let ((_let_64 (not _let_32))) (let ((_let_65 (_let_64))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_32))) (REFL :args (_let_63)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_56) :args ((or _let_27 _let_64 _let_54))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_49) _let_48 _let_58 :args (_let_55 true _let_28 false _let_8)) _let_53 :args (_let_64 true _let_27 false _let_33)) :args (_let_63 true _let_32)))) (let ((_let_67 (_let_59))) (let ((_let_68 (ASSUME :args (_let_6)))) (let ((_let_69 (ASSUME :args (_let_3)))) (let ((_let_70 (ASSUME :args (_let_62)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_68 _let_69 _let_70) :args (_let_3 _let_62 _let_6)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_70)) (CONG (REFL :args (_let_4)) (SYMM _let_69) :args (APPLY_UF ho_6)) (TRUE_INTRO _let_68))) :args (_let_6 _let_3 _let_62)) :args ((not (and _let_3 _let_62 _let_6)) SB_LITERAL))) (CONG (REFL :args ((not _let_3))) (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_5))) (REFL :args ((not _let_6))) :args _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_45)) :args ((or _let_59 _let_61))) _let_66 :args (_let_59 true _let_61)) :args (_let_6 false _let_59)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_61 1)) _let_66 :args (_let_62 true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_9)) :args ((or (not _let_8) _let_3 (not _let_9)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_235 QUANTIFIERS_INST_CBQI_PROP)) :args _let_24))) _let_23 :args (_let_9 false _let_10)) :args (_let_3 false _let_8 false _let_9)) :args (false false _let_6 true _let_5 false _let_3)) :args (_let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.75 )
% 0.22/0.75 % SZS output end Proof for SEV121^5
% 0.22/0.75 % cvc5---1.0.5 exiting
% 0.22/0.75 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------