TSTP Solution File: SET605^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET605^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 14:39:23 EDT 2023
% Result : Theorem 0.45s 0.70s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET605^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:39:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 %----Proving TH0
% 0.45/0.70 %------------------------------------------------------------------------------
% 0.45/0.70 % File : SET605^5 : TPTP v8.1.2. Released v4.0.0.
% 0.45/0.70 % Domain : Set Theory
% 0.45/0.70 % Problem : TPS problem BOOL-PROP-76
% 0.45/0.70 % Version : Especial.
% 0.45/0.70 % English : Trybulec's 76th Boolean property of sets
% 0.45/0.70
% 0.45/0.70 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.45/0.70 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.45/0.70 % Source : [Bro09]
% 0.45/0.70 % Names : tps_0192 [Bro09]
% 0.45/0.70 % : BOOL-PROP-76 [TPS]
% 0.45/0.70
% 0.45/0.70 % Status : Theorem
% 0.45/0.70 % Rating : 0.08 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, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.45/0.70 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.45/0.70 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.45/0.70 % Maximal formula atoms : 1 ( 2 avg)
% 0.45/0.70 % Number of connectives : 6 ( 1 ~; 1 |; 1 &; 3 @)
% 0.45/0.70 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.45/0.70 % Maximal formula depth : 3 ( 3 avg)
% 0.45/0.70 % Number of types : 2 ( 1 usr)
% 0.45/0.70 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.45/0.70 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.45/0.70 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.45/0.70 % SPC : TH0_THM_EQU_NAR
% 0.45/0.70
% 0.45/0.70 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.45/0.70 % project in the Department of Mathematical Sciences at Carnegie
% 0.45/0.70 % Mellon University. Distributed under the Creative Commons copyleft
% 0.45/0.70 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.45/0.70 % : Polymorphic definitions expanded.
% 0.45/0.70 %------------------------------------------------------------------------------
% 0.45/0.70 thf(a_type,type,
% 0.45/0.70 a: $tType ).
% 0.45/0.70
% 0.45/0.70 thf(cBOOL_PROP_76_pme,conjecture,
% 0.45/0.70 ! [X: a > $o,Y: a > $o] :
% 0.45/0.70 ( ( ^ [Xx: a] :
% 0.45/0.70 ( ( X @ Xx )
% 0.45/0.70 & ~ ( ( X @ Xx )
% 0.45/0.70 | ( Y @ Xx ) ) ) )
% 0.45/0.70 = ( ^ [Xx: a] : $false ) ) ).
% 0.45/0.70
% 0.45/0.70 %------------------------------------------------------------------------------
% 0.45/0.70 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.VIL8LBj1x3/cvc5---1.0.5_5836.p...
% 0.45/0.70 (declare-sort $$unsorted 0)
% 0.45/0.70 (declare-sort tptp.a 0)
% 0.45/0.70 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (= (lambda ((Xx tptp.a)) (let ((_let_1 (@ X Xx))) (and _let_1 (not (or _let_1 (@ Y Xx)))))) (lambda ((Xx tptp.a)) false)))))
% 0.45/0.70 (set-info :filename cvc5---1.0.5_5836)
% 0.45/0.70 (check-sat-assuming ( true ))
% 0.45/0.70 ------- get file name : TPTP file name is SET605^5
% 0.45/0.70 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5836.smt2...
% 0.45/0.70 --- Run --ho-elim --full-saturate-quant at 10...
% 0.45/0.70 % SZS status Theorem for SET605^5
% 0.45/0.70 % SZS output start Proof for SET605^5
% 0.45/0.70 (
% 0.45/0.70 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (= (lambda ((Xx tptp.a)) (let ((_let_1 (@ X Xx))) (and _let_1 (not (or _let_1 (@ Y Xx)))))) (lambda ((Xx tptp.a)) false)))))) (let ((_let_2 (forall ((BOUND_VARIABLE_624 tptp.a)) (not (ho_4 k_8 BOUND_VARIABLE_624))))) (let ((_let_3 (ho_4 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_340))) (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 ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_7 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_8 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_9 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_10 (forall ((BOUND_VARIABLE_663 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_660 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_631 tptp.a)) (not (ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_663) BOUND_VARIABLE_660) BOUND_VARIABLE_631))))) (let ((_let_11 (forall ((BOUND_VARIABLE_684 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_683 |u_(-> tptp.a Bool)|)) (= k_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_684) BOUND_VARIABLE_683))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (forall ((BOUND_VARIABLE_629 (-> tptp.a Bool)) (BOUND_VARIABLE_630 (-> tptp.a Bool)) (BOUND_VARIABLE_631 tptp.a)) (not (ll_3 BOUND_VARIABLE_629 BOUND_VARIABLE_630 BOUND_VARIABLE_631))))) (let ((_let_14 (forall ((BOUND_VARIABLE_624 tptp.a)) (not (ll_2 BOUND_VARIABLE_624))))) (let ((_let_15 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (= ll_2 (@ (@ ll_3 X) Y)))))) (let ((_let_16 (and _let_15 _let_14 _let_13))) (let ((_let_17 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (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))) (= (lambda ((Xx tptp.a)) (let ((_let_1 (@ X Xx))) (and _let_1 (not (or _let_1 (@ Y Xx)))))) (lambda ((BOUND_VARIABLE_599 tptp.a)) false)))) _let_15))))) (PREPROCESS :args ((and _let_14 _let_13)))) :args (_let_16)) (PREPROCESS :args ((= _let_16 (and _let_12 _let_2 _let_10))))) (PREPROCESS :args ((and _let_9 _let_8 _let_7 _let_6 _let_5 _let_4)))) :args ((and _let_12 _let_2 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4))))) (let ((_let_18 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_19 (ho_4 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_340))) (let ((_let_20 (= _let_19 _let_3))) (let ((_let_21 (forall ((z tptp.a)) (= (ho_4 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) z) (ho_4 k_8 z))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (= k_8 _let_18))) (let ((_let_24 (not _let_21))) (let ((_let_25 (or _let_24 _let_23))) (let ((_let_26 (_let_5))) (let ((_let_27 (not _let_23))) (let ((_let_28 (or))) (let ((_let_29 (_let_12))) (let ((_let_30 (_let_24))) (let ((_let_31 (_let_10))) (let ((_let_32 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_340 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_20)) :args ((or _let_19 _let_3 _let_20))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_340 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_31)) (AND_ELIM _let_17 :args (2)) :args ((not _let_19) false _let_10)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_30)) :args _let_30)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_21))) (REFL :args (_let_22)) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_23 _let_24 (not _let_25)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_29)) :args _let_29)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) (REFL :args (_let_27)) :args _let_28)) (AND_ELIM _let_17 :args (0)) :args (_let_27 true _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args (_let_18 k_8 QUANTIFIERS_INST_ENUM)) :args _let_26))) (AND_ELIM _let_17 :args (7)) :args (_let_25 false _let_5)) :args (_let_24 true _let_23 false _let_25)) :args (_let_22 true _let_21)) :args (_let_3 true _let_19 true _let_20)) (AND_ELIM _let_17 :args (1)) :args (false false _let_3 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))
% 0.45/0.70 )
% 0.45/0.70 % SZS output end Proof for SET605^5
% 0.45/0.70 % cvc5---1.0.5 exiting
% 0.55/0.70 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------