TSTP Solution File: SET027^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET027^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 14:36:58 EDT 2023
% Result : Theorem 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET027^5 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:39:11 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 % File : SET027^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.51 % Domain : Set Theory
% 0.20/0.51 % Problem : TPS problem BOOL-PROP-29
% 0.20/0.51 % Version : Especial.
% 0.20/0.51 % English : Trybulec's 29th Boolean property of sets
% 0.20/0.51
% 0.20/0.51 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.51 % : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.20/0.51 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.51 % Source : [Bro09]
% 0.20/0.51 % Names : tps_0140 [Bro09]
% 0.20/0.51 % : tps_0141 [Bro09]
% 0.20/0.51 % : 3 [Bar92]
% 0.20/0.51 % : GAZING-THM3 [TPS]
% 0.20/0.51 % : BOOL-PROP-29 [TPS]
% 0.20/0.51
% 0.20/0.51 % Status : Theorem
% 0.20/0.51 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.20/0.51 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.51 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.51 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.51 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 6 @)
% 0.20/0.51 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.51 % Maximal formula depth : 9 ( 9 avg)
% 0.20/0.51 % Number of types : 2 ( 1 usr)
% 0.20/0.51 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.51 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.51 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.20/0.51 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.51
% 0.20/0.51 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.51 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.51 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.51 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.51 % : Polymorphic definitions expanded.
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 thf(a_type,type,
% 0.20/0.51 a: $tType ).
% 0.20/0.51
% 0.20/0.51 thf(cBOOL_PROP_29_pme,conjecture,
% 0.20/0.51 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.20/0.51 ( ( ! [Xx: a] :
% 0.20/0.51 ( ( X @ Xx )
% 0.20/0.51 => ( Y @ Xx ) )
% 0.20/0.51 & ! [Xx: a] :
% 0.20/0.51 ( ( Y @ Xx )
% 0.20/0.51 => ( Z @ Xx ) ) )
% 0.20/0.51 => ! [Xx: a] :
% 0.20/0.51 ( ( X @ Xx )
% 0.20/0.51 => ( Z @ Xx ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.It8Ug9OD1f/cvc5---1.0.5_1886.p...
% 0.20/0.51 (declare-sort $$unsorted 0)
% 0.20/0.51 (declare-sort tptp.a 0)
% 0.20/0.51 (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)) (=> (@ Y Xx) (@ Z Xx)))) (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Z Xx)))))))
% 0.20/0.51 (set-info :filename cvc5---1.0.5_1886)
% 0.20/0.51 (check-sat-assuming ( true ))
% 0.20/0.51 ------- get file name : TPTP file name is SET027^5
% 0.20/0.51 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1886.smt2...
% 0.20/0.51 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.51 % SZS status Theorem for SET027^5
% 0.20/0.51 % SZS output start Proof for SET027^5
% 0.20/0.51 (
% 0.20/0.51 (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)) (=> (@ Y Xx) (@ Z Xx)))) (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Z Xx)))))))) (let ((_let_2 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_4 (not _let_3))) (let ((_let_5 (or _let_4 _let_2))) (let ((_let_6 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_7 (not _let_6))) (let ((_let_8 (forall ((Xx tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))))) (let ((_let_9 (not _let_8))) (let ((_let_10 (forall ((Xx tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx))))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9 _let_7 _let_2))) (let ((_let_13 (forall ((BOUND_VARIABLE_636 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_640 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_632 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_619 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_636 Xx)) (ho_2 BOUND_VARIABLE_640 Xx)))) (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_640 Xx)) (ho_2 BOUND_VARIABLE_632 Xx)))) (not (ho_2 BOUND_VARIABLE_636 BOUND_VARIABLE_619)) (ho_2 BOUND_VARIABLE_632 BOUND_VARIABLE_619))))) (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_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_16 (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_17 (not _let_13))) (let ((_let_18 (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)) (BOUND_VARIABLE_619 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (not (forall ((Xx tptp.a)) (or (not (@ Y Xx)) (@ Z Xx)))) (not (@ X BOUND_VARIABLE_619)) (@ Z BOUND_VARIABLE_619)))) _let_17))))))) (let ((_let_19 (or))) (let ((_let_20 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_18) :args (_let_17))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_13))) (REFL :args (_let_14)) :args _let_19)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_18 (PREPROCESS :args ((and _let_16 _let_15)))) :args ((and _let_17 _let_16 _let_15))) :args (0)) :args (_let_14 true _let_13)))) (let ((_let_21 (REFL :args (_let_12)))) (let ((_let_22 (_let_8))) (let ((_let_23 (or _let_7 _let_3))) (let ((_let_24 (_let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_5)) :args ((or _let_2 _let_4 (not _let_5)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_7 _let_3 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 2)) (CONG _let_21 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_19)) :args ((or _let_6 _let_12))) _let_20 :args (_let_6 true _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_24) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx) false))))) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 0)) (CONG _let_21 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_19)) :args ((or _let_10 _let_12))) _let_20 :args (_let_10 true _let_12)) :args (_let_23 false _let_10)) :args (_let_3 false _let_6 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_22) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx) true))))) :args _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 1)) (CONG _let_21 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_19)) :args ((or _let_8 _let_12))) _let_20 :args (_let_8 true _let_12)) :args (_let_5 false _let_8)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_12 3)) _let_20 :args ((not _let_2) true _let_12)) :args (false false _let_3 false _let_5 true _let_2)) :args (_let_1 true)))))))))))))))))))))))))))
% 0.20/0.52 )
% 0.20/0.52 % SZS output end Proof for SET027^5
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------