TSTP Solution File: SET201^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET201^5 : 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 14:38:12 EDT 2023
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET201^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sat Aug 26 09:28:56 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.20/0.47 %----Proving TH0
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 % File : SET201^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.50 % Domain : Set Theory
% 0.20/0.50 % Problem : TPS problem BOOL-PROP-41
% 0.20/0.50 % Version : Especial.
% 0.20/0.50 % English : Trybulec's 41st Boolean property of sets
% 0.20/0.50
% 0.20/0.50 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.50 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.50 % Source : [Bro09]
% 0.20/0.50 % Names : tps_0254 [Bro09]
% 0.20/0.50 % : BOOL-PROP-41 [TPS]
% 0.20/0.50
% 0.20/0.50 % Status : Theorem
% 0.20/0.50 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.20/0.50 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.50 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.20/0.50 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.50 % Number of connectives : 15 ( 0 ~; 0 |; 3 &; 8 @)
% 0.20/0.50 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.50 % Maximal formula depth : 9 ( 9 avg)
% 0.20/0.50 % Number of types : 2 ( 1 usr)
% 0.20/0.50 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.50 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.20/0.50 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.20/0.50 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.50
% 0.20/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.50 % : Polymorphic definitions expanded.
% 0.20/0.50 % :
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 thf(a_type,type,
% 0.20/0.50 a: $tType ).
% 0.20/0.50
% 0.20/0.50 thf(cV,type,
% 0.20/0.50 cV: a > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cBOOL_PROP_41_pme,conjecture,
% 0.20/0.50 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.20/0.50 ( ( ! [Xx: a] :
% 0.20/0.50 ( ( X @ Xx )
% 0.20/0.50 => ( Y @ Xx ) )
% 0.20/0.50 & ! [Xx: a] :
% 0.20/0.50 ( ( Z @ Xx )
% 0.20/0.50 => ( cV @ Xx ) ) )
% 0.20/0.50 => ! [Xx: a] :
% 0.20/0.50 ( ( ( X @ Xx )
% 0.20/0.50 & ( Z @ Xx ) )
% 0.20/0.50 => ( ( Y @ Xx )
% 0.20/0.50 & ( cV @ Xx ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.o7yz6OM65i/cvc5---1.0.5_20282.p...
% 0.20/0.50 (declare-sort $$unsorted 0)
% 0.20/0.50 (declare-sort tptp.a 0)
% 0.20/0.50 (declare-fun tptp.cV (tptp.a) Bool)
% 0.20/0.50 (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)) (=> (@ Z Xx) (@ tptp.cV Xx)))) (forall ((Xx tptp.a)) (=> (and (@ X Xx) (@ Z Xx)) (and (@ Y Xx) (@ tptp.cV Xx))))))))
% 0.20/0.50 (set-info :filename cvc5---1.0.5_20282)
% 0.20/0.50 (check-sat-assuming ( true ))
% 0.20/0.50 ------- get file name : TPTP file name is SET201^5
% 0.20/0.50 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20282.smt2...
% 0.20/0.50 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.50 % SZS status Theorem for SET201^5
% 0.20/0.50 % SZS output start Proof for SET201^5
% 0.20/0.50 (
% 0.20/0.50 (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)) (=> (@ Z Xx) (@ tptp.cV Xx)))) (forall ((Xx tptp.a)) (=> (and (@ X Xx) (@ Z Xx)) (and (@ Y Xx) (@ tptp.cV Xx))))))))) (let ((_let_2 (forall ((Xx tptp.a)) (or (not (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Xx)) (ho_3 k_2 Xx))))) (let ((_let_3 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_5 (not _let_4))) (let ((_let_6 (or _let_5 _let_3))) (let ((_let_7 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (and _let_7 _let_3))) (let ((_let_9 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_10 (not _let_9))) (let ((_let_11 (not _let_2))) (let ((_let_12 (forall ((Xx tptp.a)) (or (not (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)) (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11 _let_10 _let_5 _let_8))) (let ((_let_15 (forall ((BOUND_VARIABLE_654 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_648 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_651 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_627 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (ho_3 BOUND_VARIABLE_654 Xx)) (ho_3 BOUND_VARIABLE_648 Xx)))) (not (forall ((Xx tptp.a)) (or (not (ho_3 BOUND_VARIABLE_651 Xx)) (ho_3 k_2 Xx)))) (not (ho_3 BOUND_VARIABLE_654 BOUND_VARIABLE_627)) (not (ho_3 BOUND_VARIABLE_651 BOUND_VARIABLE_627)) (and (ho_3 BOUND_VARIABLE_648 BOUND_VARIABLE_627) (ho_3 k_2 BOUND_VARIABLE_627)))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_19 (not _let_15))) (let ((_let_20 (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_627 tptp.a)) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (not (forall ((Xx tptp.a)) (or (not (@ Z Xx)) (@ tptp.cV Xx)))) (not (@ X BOUND_VARIABLE_627)) (not (@ Z BOUND_VARIABLE_627)) (and (@ Y BOUND_VARIABLE_627) (@ tptp.cV BOUND_VARIABLE_627))))) _let_19))))))) (let ((_let_21 (or))) (let ((_let_22 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_20) :args (_let_19))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) (REFL :args (_let_16)) :args _let_21)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_20 (PREPROCESS :args ((and _let_18 _let_17)))) :args ((and _let_19 _let_18 _let_17))) :args (0)) :args (_let_16 true _let_15)))) (let ((_let_23 (REFL :args (_let_14)))) (let ((_let_24 (not _let_6))) (let ((_let_25 (or _let_10 _let_7))) (let ((_let_26 (_let_12))) (let ((_let_27 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_28 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_28) :args _let_27) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_5 _let_3 _let_24))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 3)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_21)) :args ((or _let_4 _let_14))) _let_22 :args (_let_4 true _let_14)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_8)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 4)) _let_22 :args ((not _let_8) true _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_10 _let_7 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 2)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_21)) :args ((or _let_9 _let_14))) _let_22 :args (_let_9 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args _let_27) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_21)) :args ((or _let_12 _let_14))) _let_22 :args (_let_12 true _let_14)) :args (_let_25 false _let_12)) :args (_let_7 false _let_9 false _let_25)) :args ((not _let_3) true _let_8 false _let_7)) :args (_let_24 false _let_4 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 1)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_2))) :args _let_21)) :args ((or _let_2 _let_14))) _let_22 :args (_let_2 true _let_14)) :args (false true _let_6 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))
% 0.20/0.51 )
% 0.20/0.51 % SZS output end Proof for SET201^5
% 0.20/0.51 % cvc5---1.0.5 exiting
% 0.20/0.51 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------