TSTP Solution File: SET593^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET593^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 14:39:17 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
% 0.00/0.12 % Problem : SET593^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:47:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 % File : SET593^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.51 % Domain : Set Theory
% 0.20/0.51 % Problem : TPS problem BOOL-PROP-52
% 0.20/0.51 % Version : Especial.
% 0.20/0.51 % English : Trybulec's 52nd Boolean property of sets
% 0.20/0.51
% 0.20/0.51 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.51 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.51 % Source : [Bro09]
% 0.20/0.51 % Names : tps_0264 [Bro09]
% 0.20/0.51 % : BOOL-PROP-52 [TPS]
% 0.20/0.51
% 0.20/0.51 % Status : Theorem
% 0.20/0.51 % Rating : 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 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 : 19 ( 2 ~; 1 |; 3 &; 9 @)
% 0.20/0.51 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.51 % Maximal formula depth : 11 ( 11 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_52_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 | ( Z @ Xx ) ) )
% 0.20/0.51 => ( ! [Xx: a] :
% 0.20/0.51 ( ( ( X @ Xx )
% 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 => ( Y @ Xx ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.k0IlhSy7Wt/cvc5---1.0.5_7200.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))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (or (@ Y Xx) (@ Z Xx)))) (and (forall ((Xx tptp.a)) (=> (and (@ X Xx) (not (@ Y Xx))) (@ Z Xx))) (forall ((Xx tptp.a)) (=> (and (@ X Xx) (not (@ Z Xx))) (@ Y Xx))))))))
% 0.20/0.51 (set-info :filename cvc5---1.0.5_7200)
% 0.20/0.51 (check-sat-assuming ( true ))
% 0.20/0.51 ------- get file name : TPTP file name is SET593^5
% 0.20/0.51 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7200.smt2...
% 0.20/0.51 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.51 % SZS status Theorem for SET593^5
% 0.20/0.51 % SZS output start Proof for SET593^5
% 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))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (or (@ Y Xx) (@ Z Xx)))) (and (forall ((Xx tptp.a)) (=> (and (@ X Xx) (not (@ Y Xx))) (@ Z Xx))) (forall ((Xx tptp.a)) (=> (and (@ X Xx) (not (@ Z Xx))) (@ Y Xx))))))))) (let ((_let_2 (forall ((Xx tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_4 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_5 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_6 (not _let_5))) (let ((_let_7 (or _let_6 _let_4 _let_3))) (let ((_let_8 (or _let_6 _let_3 _let_4))) (let ((_let_9 (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_10 (and _let_9 _let_8))) (let ((_let_11 (not _let_2))) (let ((_let_12 (or _let_11 _let_10))) (let ((_let_13 (forall ((BOUND_VARIABLE_654 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_648 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_652 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_635 tptp.a) (BOUND_VARIABLE_628 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_654 Xx)) (ho_2 BOUND_VARIABLE_648 Xx) (ho_2 BOUND_VARIABLE_652 Xx)))) (and (or (not (ho_2 BOUND_VARIABLE_654 BOUND_VARIABLE_628)) (ho_2 BOUND_VARIABLE_648 BOUND_VARIABLE_628) (ho_2 BOUND_VARIABLE_652 BOUND_VARIABLE_628)) (or (not (ho_2 BOUND_VARIABLE_654 BOUND_VARIABLE_635)) (ho_2 BOUND_VARIABLE_652 BOUND_VARIABLE_635) (ho_2 BOUND_VARIABLE_648 BOUND_VARIABLE_635))))))) (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_635 tptp.a) (BOUND_VARIABLE_628 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx) (@ Z Xx)))) (and (or (not (@ X BOUND_VARIABLE_628)) (@ Y BOUND_VARIABLE_628) (@ Z BOUND_VARIABLE_628)) (or (not (@ X BOUND_VARIABLE_635)) (@ Z BOUND_VARIABLE_635) (@ Y BOUND_VARIABLE_635)))))) _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 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 0)) (CONG (REFL :args (_let_12)) (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_2))) :args _let_19)) :args ((or _let_2 _let_12))) _let_20 :args (_let_2 true _let_12)))) (let ((_let_22 (not _let_7))) (let ((_let_23 (_let_2))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_10)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_12 1)) _let_20 :args ((not _let_10) true _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_23)) _let_21 :args (_let_9 false _let_2)) :args ((not _let_8) true _let_10 false _let_9)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_6 _let_3 _let_4 _let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_8 0)) (CONG (REFL :args (_let_8)) (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_19)) :args ((or _let_5 _let_8))) _let_25 :args (_let_5 true _let_8)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_8 1)) _let_25 :args ((not _let_3) true _let_8)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_8 2)) _let_25 :args ((not _let_4) true _let_8)) :args (_let_22 false _let_5 true _let_3 true _let_4)) _let_21 :args (false true _let_7 false _let_2)) :args (_let_1 true))))))))))))))))))))))))))))
% 0.20/0.52 )
% 0.20/0.52 % SZS output end Proof for SET593^5
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------