TSTP Solution File: SET584^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET584^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 14:39:12 EDT 2023
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET584^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.17/0.35 % Computer : n016.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 15:25:12 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : SET584^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.52 % Domain : Set Theory
% 0.21/0.52 % Problem : TPS problem BOOL-PROP-33
% 0.21/0.52 % Version : Especial.
% 0.21/0.52 % English : Trybulec's 33rd Boolean property of sets
% 0.21/0.52
% 0.21/0.52 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.21/0.52 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.52 % Source : [Bro09]
% 0.21/0.52 % Names : tps_0133 [Bro09]
% 0.21/0.52 % : BOOL-PROP-33 [TPS]
% 0.21/0.52
% 0.21/0.52 % Status : Theorem
% 0.21/0.52 % Rating : 0.00 v4.0.0
% 0.21/0.52 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.21/0.52 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.52 % Number of connectives : 11 ( 0 ~; 2 |; 0 &; 6 @)
% 0.21/0.52 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 9 ( 9 avg)
% 0.21/0.52 % Number of types : 2 ( 1 usr)
% 0.21/0.52 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.52 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.21/0.52 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.52
% 0.21/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.52 % : Polymorphic definitions expanded.
% 0.21/0.52 % :
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(a_type,type,
% 0.21/0.52 a: $tType ).
% 0.21/0.52
% 0.21/0.52 thf(cBOOL_PROP_33_pme,conjecture,
% 0.21/0.52 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.21/0.52 ( ! [Xx: a] :
% 0.21/0.52 ( ( X @ Xx )
% 0.21/0.52 => ( Y @ Xx ) )
% 0.21/0.52 => ! [Xx: a] :
% 0.21/0.52 ( ( ( X @ Xx )
% 0.21/0.52 | ( Z @ Xx ) )
% 0.21/0.52 => ( ( Y @ Xx )
% 0.21/0.52 | ( Z @ Xx ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QcZuyQ9yQO/cvc5---1.0.5_29810.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-sort tptp.a 0)
% 0.21/0.52 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (forall ((Xx tptp.a)) (let ((_let_1 (@ Z Xx))) (=> (or (@ X Xx) _let_1) (or (@ Y Xx) _let_1))))))))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_29810)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is SET584^5
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29810.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for SET584^5
% 0.21/0.52 % SZS output start Proof for SET584^5
% 0.21/0.52 (
% 0.21/0.52 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (forall ((Xx tptp.a)) (let ((_let_1 (@ Z Xx))) (=> (or (@ X Xx) _let_1) (or (@ Y Xx) _let_1))))))))) (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))))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_4 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_5 (not _let_4))) (let ((_let_6 (or _let_5 _let_3))) (let ((_let_7 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (not _let_7))) (let ((_let_9 (and _let_5 _let_8))) (let ((_let_10 (not _let_2))) (let ((_let_11 (or _let_10 _let_9 _let_3 _let_7))) (let ((_let_12 (forall ((BOUND_VARIABLE_634 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_631 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_627 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_611 tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_627 BOUND_VARIABLE_611))) (or (not (forall ((Xx tptp.a)) (or (not (ho_2 BOUND_VARIABLE_634 Xx)) (ho_2 BOUND_VARIABLE_631 Xx)))) (and (not (ho_2 BOUND_VARIABLE_634 BOUND_VARIABLE_611)) (not _let_1)) (ho_2 BOUND_VARIABLE_631 BOUND_VARIABLE_611) _let_1))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (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_15 (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_16 (not _let_12))) (let ((_let_17 (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_611 tptp.a)) (let ((_let_1 (@ Z BOUND_VARIABLE_611))) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (and (not (@ X BOUND_VARIABLE_611)) (not _let_1)) (@ Y BOUND_VARIABLE_611) _let_1)))) _let_16))))))) (let ((_let_18 (or))) (let ((_let_19 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_17) :args (_let_16))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_12))) (REFL :args (_let_13)) :args _let_18)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_17 (PREPROCESS :args ((and _let_15 _let_14)))) :args ((and _let_16 _let_15 _let_14))) :args (0)) :args (_let_13 true _let_12)))) (let ((_let_20 (not _let_6))) (let ((_let_21 (_let_9))) (let ((_let_22 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_22) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_5 _let_3 _let_20))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_21) (CONG (REFL :args _let_21) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_18)) :args ((or _let_4 _let_7 _let_9))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_11 3)) :args ((or _let_8 _let_11))) _let_19 :args (_let_8 true _let_11)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_11 1)) _let_19 :args ((not _let_9) true _let_11)) :args (_let_4 true _let_7 true _let_9)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_11 2)) _let_19 :args ((not _let_3) true _let_11)) :args (_let_20 false _let_4 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_2))) :args _let_18)) :args ((or _let_2 _let_11))) _let_19 :args (_let_2 true _let_11)) :args (false true _let_6 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for SET584^5
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------