TSTP Solution File: SET632^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET632^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 14:39:39 EDT 2023
% Result : Theorem 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET632^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n007.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 : Sat Aug 26 11:34:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 % File : SET632^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.54 % Domain : Set Theory
% 0.22/0.54 % Problem : TPS problem BOOL-PROP-114
% 0.22/0.54 % Version : Especial.
% 0.22/0.54 % English : Trybulec's 114th Boolean property of sets
% 0.22/0.54
% 0.22/0.54 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.22/0.54 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.54 % Source : [Bro09]
% 0.22/0.54 % Names : tps_0315 [Bro09]
% 0.22/0.54 % : BOOL-PROP-114 [TPS]
% 0.22/0.54
% 0.22/0.54 % Status : Theorem
% 0.22/0.54 % Rating : 0.23 v8.1.0, 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, 0.00 v6.1.0, 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
% 0.22/0.54 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.22/0.54 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.22/0.54 % Maximal formula atoms : 1 ( 2 avg)
% 0.22/0.54 % Number of connectives : 13 ( 1 ~; 0 |; 3 &; 6 @)
% 0.22/0.54 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.22/0.54 % Maximal formula depth : 11 ( 11 avg)
% 0.22/0.54 % Number of types : 2 ( 1 usr)
% 0.22/0.54 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.22/0.54 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.22/0.54 % Number of variables : 7 ( 1 ^; 5 !; 1 ?; 7 :)
% 0.22/0.54 % SPC : TH0_THM_EQU_NAR
% 0.22/0.54
% 0.22/0.54 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.54 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.54 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.54 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.54 % : Polymorphic definitions expanded.
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 thf(a_type,type,
% 0.22/0.54 a: $tType ).
% 0.22/0.54
% 0.22/0.54 thf(cBOOL_PROP_114_pme,conjecture,
% 0.22/0.54 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.22/0.54 ( ( ! [Xx: a] :
% 0.22/0.54 ( ( X @ Xx )
% 0.22/0.54 => ( Y @ Xx ) )
% 0.22/0.54 & ! [Xx: a] :
% 0.22/0.54 ( ( X @ Xx )
% 0.22/0.54 => ( Z @ Xx ) )
% 0.22/0.54 & ~ ? [Xx: a] :
% 0.22/0.54 ( ( Y @ Xx )
% 0.22/0.54 & ( Z @ Xx ) ) )
% 0.22/0.54 => ( X
% 0.22/0.54 = ( ^ [Xx: a] : $false ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.zkf6BPq6Da/cvc5---1.0.5_2518.p...
% 0.22/0.54 (declare-sort $$unsorted 0)
% 0.22/0.54 (declare-sort tptp.a 0)
% 0.22/0.54 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (=> (and (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Z Xx))) (not (exists ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) (= X (lambda ((Xx tptp.a)) false))))))
% 0.22/0.54 (set-info :filename cvc5---1.0.5_2518)
% 0.22/0.54 (check-sat-assuming ( true ))
% 0.22/0.54 ------- get file name : TPTP file name is SET632^5
% 0.22/0.54 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2518.smt2...
% 0.22/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.54 % SZS status Theorem for SET632^5
% 0.22/0.54 % SZS output start Proof for SET632^5
% 0.22/0.54 (
% 0.22/0.54 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (=> (and (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Z Xx))) (not (exists ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) (= X (lambda ((Xx tptp.a)) false))))))) (let ((_let_2 (forall ((BOUND_VARIABLE_645 tptp.a)) (not (ho_4 k_3 BOUND_VARIABLE_645))))) (let ((_let_3 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_4 (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_5 (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_6 (forall ((BOUND_VARIABLE_661 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_666 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_663 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xx tptp.a)) (or (not (ho_4 BOUND_VARIABLE_661 Xx)) (ho_4 BOUND_VARIABLE_666 Xx)))) (not (forall ((Xx tptp.a)) (or (not (ho_4 BOUND_VARIABLE_661 Xx)) (ho_4 BOUND_VARIABLE_663 Xx)))) (not (forall ((Xx tptp.a)) (or (not (ho_4 BOUND_VARIABLE_666 Xx)) (not (ho_4 BOUND_VARIABLE_663 Xx))))) (= k_3 BOUND_VARIABLE_661))))) (let ((_let_7 (not _let_6))) (let ((_let_8 (forall ((BOUND_VARIABLE_645 tptp.a)) (not (ll_2 BOUND_VARIABLE_645))))) (let ((_let_9 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Z Xx)))) (not (forall ((Xx tptp.a)) (or (not (@ Y Xx)) (not (@ Z Xx))))) (= X ll_2)))))) (let ((_let_10 (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 (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Z Xx)))) (not (forall ((Xx tptp.a)) (or (not (@ Y Xx)) (not (@ Z Xx))))) (= X (lambda ((BOUND_VARIABLE_636 tptp.a)) false))))) _let_9))))) (PREPROCESS :args (_let_8))) (PREPROCESS :args ((= (and _let_9 _let_8) (and _let_7 _let_2))))) (PREPROCESS :args ((and _let_5 _let_4)))) :args ((and _let_7 _let_2 _let_5 _let_4))))) (let ((_let_11 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_12 (= _let_11 _let_3))) (let ((_let_13 (forall ((z tptp.a)) (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 z) (ho_4 k_3 z))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (= k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (not _let_13))) (let ((_let_17 (or _let_16 _let_15))) (let ((_let_18 (_let_5))) (let ((_let_19 (forall ((Xx tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Xx)) (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx)))))) (let ((_let_20 (not _let_19))) (let ((_let_21 (forall ((Xx tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx)) (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (forall ((Xx tptp.a)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx)) (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Xx))))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_20 _let_15))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or))) (let ((_let_28 (_let_7))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_28)) :args _let_28)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) (REFL :args (_let_26)) :args _let_27)) (AND_ELIM _let_10 :args (0)) :args (_let_26 true _let_6)))) (let ((_let_30 (_let_16))) (let ((_let_31 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_32 (not _let_11))) (let ((_let_33 (or _let_32 _let_31))) (let ((_let_34 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_35 (or _let_32 _let_34))) (let ((_let_36 (not _let_34))) (let ((_let_37 (not _let_31))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (REFL :args (_let_25)))) (let ((_let_40 (_let_23))) (let ((_let_41 (_let_21))) (let ((_let_42 (_let_19))) (let ((_let_43 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_44 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args _let_43) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_12)) :args ((or _let_11 _let_3 _let_12))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_36 (not _let_38)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args _let_43) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_27)) :args ((or _let_19 _let_25))) _let_29 :args (_let_19 true _let_25)) :args (_let_38 false _let_19)) (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_32 _let_34 (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx) false))))) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_27)) :args ((or _let_21 _let_25))) _let_29 :args (_let_21 true _let_25)) :args (_let_35 false _let_21)) (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_31 (not _let_33)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_40) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx) false))))) :args _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_27)) :args ((or _let_23 _let_25))) _let_29 :args (_let_23 true _let_25)) :args (_let_33 false _let_23)) :args (_let_32 false _let_38 false _let_34 false _let_35 false _let_31 false _let_33)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_30)) :args _let_30)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_13))) (REFL :args (_let_14)) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_15 _let_16 (not _let_17)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 3)) _let_29 :args ((not _let_15) true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_18) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 k_3 QUANTIFIERS_INST_ENUM)) :args _let_18))) (AND_ELIM _let_10 :args (2)) :args (_let_17 false _let_5)) :args (_let_16 true _let_15 false _let_17)) :args (_let_14 true _let_13)) :args (_let_3 true _let_11 true _let_12)) (AND_ELIM _let_10 :args (1)) :args (false false _let_3 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.54 )
% 0.22/0.54 % SZS output end Proof for SET632^5
% 0.22/0.54 % cvc5---1.0.5 exiting
% 0.22/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------