TSTP Solution File: SEV394^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV394^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV394^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 03:13:36 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.19/0.46 %----Proving TH0
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 % File : SEV394^5 : TPTP v8.1.2. Released v4.0.0.
% 0.19/0.52 % Domain : Set Theory
% 0.19/0.52 % Problem : TPS problem THM269
% 0.19/0.52 % Version : Especial.
% 0.19/0.52 % English : Example for CADE-15.
% 0.19/0.52
% 0.19/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.52 % Source : [Bro09]
% 0.19/0.52 % Names : tps_0317 [Bro09]
% 0.19/0.52 % : THM108 [TPS]
% 0.19/0.52 % : THM269 [TPS]
% 0.19/0.52
% 0.19/0.52 % Status : Theorem
% 0.19/0.52 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.52 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.52 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.19/0.52 % Maximal formula atoms : 1 ( 2 avg)
% 0.19/0.52 % Number of connectives : 15 ( 2 ~; 0 |; 3 &; 7 @)
% 0.19/0.52 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.52 % Maximal formula depth : 11 ( 11 avg)
% 0.19/0.52 % Number of types : 2 ( 1 usr)
% 0.19/0.52 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.52 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.19/0.52 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.19/0.52 % SPC : TH0_THM_EQU_NAR
% 0.19/0.52
% 0.19/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.52 % : Polymorphic definitions expanded.
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 thf(a_type,type,
% 0.19/0.52 a: $tType ).
% 0.19/0.52
% 0.19/0.52 thf(cTHM269_pme,conjecture,
% 0.19/0.52 ! [Xw: a > $o,Xy: a > $o,Xz: a > $o] :
% 0.19/0.52 ( ( ! [Xx: a] :
% 0.19/0.52 ( ( ( Xw @ Xx )
% 0.19/0.52 & ~ ( Xz @ Xx ) )
% 0.19/0.52 => ( Xy @ Xx ) )
% 0.19/0.52 & ( ( ^ [Xx: a] :
% 0.19/0.52 ( ( Xz @ Xx )
% 0.19/0.52 & ~ ( Xy @ Xx ) ) )
% 0.19/0.52 = ( ^ [Xx: a] : $false ) ) )
% 0.19/0.52 => ! [Xx: a] :
% 0.19/0.52 ( ( Xw @ Xx )
% 0.19/0.52 => ( Xy @ Xx ) ) ) ).
% 0.19/0.52
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.GJyfJAXj1W/cvc5---1.0.5_4369.p...
% 0.19/0.52 (declare-sort $$unsorted 0)
% 0.19/0.52 (declare-sort tptp.a 0)
% 0.19/0.52 (assert (not (forall ((Xw (-> tptp.a Bool)) (Xy (-> tptp.a Bool)) (Xz (-> tptp.a Bool))) (=> (and (forall ((Xx tptp.a)) (=> (and (@ Xw Xx) (not (@ Xz Xx))) (@ Xy Xx))) (= (lambda ((Xx tptp.a)) (and (@ Xz Xx) (not (@ Xy Xx)))) (lambda ((Xx tptp.a)) false))) (forall ((Xx tptp.a)) (=> (@ Xw Xx) (@ Xy Xx)))))))
% 0.19/0.52 (set-info :filename cvc5---1.0.5_4369)
% 0.19/0.52 (check-sat-assuming ( true ))
% 0.19/0.52 ------- get file name : TPTP file name is SEV394^5
% 0.19/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4369.smt2...
% 0.19/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.52 % SZS status Theorem for SEV394^5
% 0.19/0.52 % SZS output start Proof for SEV394^5
% 0.19/0.52 (
% 0.19/0.52 (let ((_let_1 (not (forall ((Xw (-> tptp.a Bool)) (Xy (-> tptp.a Bool)) (Xz (-> tptp.a Bool))) (=> (and (forall ((Xx tptp.a)) (=> (and (@ Xw Xx) (not (@ Xz Xx))) (@ Xy Xx))) (= (lambda ((Xx tptp.a)) (and (@ Xz Xx) (not (@ Xy Xx)))) (lambda ((Xx tptp.a)) false))) (forall ((Xx tptp.a)) (=> (@ Xw Xx) (@ Xy Xx)))))))) (let ((_let_2 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_3 (= k_8 _let_2))) (let ((_let_4 (ho_4 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_5 (ho_4 _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_6 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_7 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_8 (not _let_7))) (let ((_let_9 (not _let_3))) (let ((_let_10 (forall ((Xx tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Xx)) (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Xx) (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx))))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9 _let_8 _let_6))) (let ((_let_13 (forall ((BOUND_VARIABLE_728 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_726 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_731 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_630 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (ho_4 BOUND_VARIABLE_728 Xx)) (ho_4 BOUND_VARIABLE_731 Xx) (ho_4 BOUND_VARIABLE_726 Xx)))) (not (= k_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_731) BOUND_VARIABLE_726))) (not (ho_4 BOUND_VARIABLE_728 BOUND_VARIABLE_630)) (ho_4 BOUND_VARIABLE_726 BOUND_VARIABLE_630))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (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_16 (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_17 (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_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_18 (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_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_19 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _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)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _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_702 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_699 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_678 tptp.a)) (= (ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_702) BOUND_VARIABLE_699) BOUND_VARIABLE_678) (and (ho_4 BOUND_VARIABLE_702 BOUND_VARIABLE_678) (not (ho_4 BOUND_VARIABLE_699 BOUND_VARIABLE_678))))))) (let ((_let_22 (forall ((BOUND_VARIABLE_671 tptp.a)) (not (ho_4 k_8 BOUND_VARIABLE_671))))) (let ((_let_23 (not _let_13))) (let ((_let_24 (forall ((BOUND_VARIABLE_676 (-> tptp.a Bool)) (BOUND_VARIABLE_677 (-> tptp.a Bool)) (BOUND_VARIABLE_678 tptp.a)) (= (and (@ BOUND_VARIABLE_676 BOUND_VARIABLE_678) (not (@ BOUND_VARIABLE_677 BOUND_VARIABLE_678))) (ll_3 BOUND_VARIABLE_676 BOUND_VARIABLE_677 BOUND_VARIABLE_678))))) (let ((_let_25 (forall ((BOUND_VARIABLE_671 tptp.a)) (not (ll_2 BOUND_VARIABLE_671))))) (let ((_let_26 (not (forall ((Xw (-> tptp.a Bool)) (Xy (-> tptp.a Bool)) (Xz (-> tptp.a Bool)) (BOUND_VARIABLE_630 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (@ Xw Xx)) (@ Xz Xx) (@ Xy Xx)))) (not (= ll_2 (@ (@ ll_3 Xz) Xy))) (not (@ Xw BOUND_VARIABLE_630)) (@ Xy BOUND_VARIABLE_630)))))) (let ((_let_27 (and _let_26 _let_25 _let_24))) (let ((_let_28 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xw (-> tptp.a Bool)) (Xy (-> tptp.a Bool)) (Xz (-> tptp.a Bool)) (BOUND_VARIABLE_630 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (@ Xw Xx)) (@ Xz Xx) (@ Xy Xx)))) (not (= (lambda ((Xx tptp.a)) (and (@ Xz Xx) (not (@ Xy Xx)))) (lambda ((BOUND_VARIABLE_643 tptp.a)) false))) (not (@ Xw BOUND_VARIABLE_630)) (@ Xy BOUND_VARIABLE_630)))) _let_26))))) (PREPROCESS :args ((and _let_25 _let_24)))) :args (_let_27)) (PREPROCESS :args ((= _let_27 (and _let_23 _let_22 _let_21))))) (PREPROCESS :args ((and _let_20 _let_19 _let_18 _let_17 _let_16 _let_15)))) :args ((and _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15))))) (let ((_let_29 (or))) (let ((_let_30 (_let_23))) (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_23) _let_13))) (REFL :args (_let_14)) :args _let_29)) (AND_ELIM _let_28 :args (0)) :args (_let_14 true _let_13)))) (let ((_let_32 (REFL :args (_let_12)))) (let ((_let_33 (not _let_4))) (let ((_let_34 (_let_22))) (let ((_let_35 (not _let_6))) (let ((_let_36 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_37 (and _let_36 _let_35))) (let ((_let_38 (= _let_5 _let_37))) (let ((_let_39 (_let_21))) (let ((_let_40 (or _let_8 _let_36 _let_6))) (let ((_let_41 (_let_10))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_12 3)) _let_31 :args (_let_35 true _let_12)))) (let ((_let_43 (not _let_36))) (let ((_let_44 (_let_37))) (let ((_let_45 (ASSUME :args (_let_5)))) (let ((_let_46 (ASSUME :args (_let_3)))) (let ((_let_47 (ASSUME :args (_let_33)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_45 _let_46 _let_47) :args (_let_3 _let_33 _let_5)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_47)) (CONG (SYMM (SYMM _let_46)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) :args (APPLY_UF ho_4)) (TRUE_INTRO _let_45))) :args (_let_5 _let_3 _let_33)) :args ((not (and _let_3 _let_33 _let_5)) SB_LITERAL))) (CONG (REFL :args (_let_9)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_4))) (REFL :args ((not _let_5))) :args _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_38)) :args ((or _let_5 (not _let_37) (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_44) (CONG (REFL :args _let_44) (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_6))) :args _let_29)) :args ((or _let_6 _let_43 _let_37))) _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_8 _let_6 _let_36 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 2)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_29)) :args ((or _let_7 _let_12))) _let_31 :args (_let_7 true _let_12)) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Xx) false))))) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 0)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_29)) :args ((or _let_10 _let_12))) _let_31 :args (_let_10 true _let_12)) :args (_let_40 false _let_10)) :args (_let_36 false _let_7 true _let_6 false _let_40)) :args (_let_37 true _let_6 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_39)) (AND_ELIM _let_28 :args (2)) :args (_let_38 false _let_21)) :args (_let_5 false _let_37 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_34) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_ENUM)) :args _let_34)) (AND_ELIM _let_28 :args (1)) :args (_let_33 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_3))) :args _let_29)) :args ((or _let_3 _let_12))) _let_31 :args (_let_3 true _let_12)) :args (false false _let_5 true _let_4 false _let_3)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.52 )
% 0.19/0.52 % SZS output end Proof for SEV394^5
% 0.19/0.52 % cvc5---1.0.5 exiting
% 0.19/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------