TSTP Solution File: SET618^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET618^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 14:39:31 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET618^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n018.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 10:48:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.56 %------------------------------------------------------------------------------
% 0.20/0.56 % File : SET618^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.56 % Domain : Set Theory
% 0.20/0.56 % Problem : TPS problem BOOL-PROP-93
% 0.20/0.56 % Version : Especial.
% 0.20/0.56 % English : Trybulec's 93th Boolean property of sets
% 0.20/0.56
% 0.20/0.56 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.56 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.56 % Source : [Bro09]
% 0.20/0.56 % Names : tps_0201 [Bro09]
% 0.20/0.56 % : BOOL-PROP-93 [TPS]
% 0.20/0.56
% 0.20/0.56 % Status : Theorem
% 0.20/0.56 % 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 v4.0.0
% 0.20/0.56 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.20/0.56 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.20/0.56 % Maximal formula atoms : 1 ( 2 avg)
% 0.20/0.56 % Number of connectives : 9 ( 2 ~; 1 |; 2 &; 4 @)
% 0.20/0.56 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.56 % Maximal formula depth : 2 ( 2 avg)
% 0.20/0.56 % Number of types : 2 ( 1 usr)
% 0.20/0.56 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.20/0.56 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.20/0.56 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.20/0.56 % SPC : TH0_THM_EQU_NAR
% 0.20/0.56
% 0.20/0.56 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.56 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.56 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.56 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.56 % : Polymorphic definitions expanded.
% 0.20/0.56 %------------------------------------------------------------------------------
% 0.20/0.56 thf(a_type,type,
% 0.20/0.56 a: $tType ).
% 0.20/0.56
% 0.20/0.56 thf(cBOOL_PROP_93_pme,conjecture,
% 0.20/0.56 ! [X: a > $o] :
% 0.20/0.56 ( ( ^ [Xz: a] :
% 0.20/0.56 ( ( ( X @ Xz )
% 0.20/0.56 & ~ ( X @ Xz ) )
% 0.20/0.56 | ( ( X @ Xz )
% 0.20/0.56 & ~ ( X @ Xz ) ) ) )
% 0.20/0.56 = ( ^ [Xx: a] : $false ) ) ).
% 0.20/0.56
% 0.20/0.56 %------------------------------------------------------------------------------
% 0.20/0.56 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.EH3nLsDE5t/cvc5---1.0.5_5129.p...
% 0.20/0.56 (declare-sort $$unsorted 0)
% 0.20/0.56 (declare-sort tptp.a 0)
% 0.20/0.56 (assert (not (forall ((X (-> tptp.a Bool))) (= (lambda ((Xz tptp.a)) (let ((_let_1 (@ X Xz))) (let ((_let_2 (and _let_1 (not _let_1)))) (or _let_2 _let_2)))) (lambda ((Xx tptp.a)) false)))))
% 0.20/0.56 (set-info :filename cvc5---1.0.5_5129)
% 0.20/0.56 (check-sat-assuming ( true ))
% 0.20/0.56 ------- get file name : TPTP file name is SET618^5
% 0.20/0.56 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5129.smt2...
% 0.20/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.56 % SZS status Theorem for SET618^5
% 0.20/0.56 % SZS output start Proof for SET618^5
% 0.20/0.56 (
% 0.20/0.56 (let ((_let_1 (not (forall ((X (-> tptp.a Bool))) (= (lambda ((Xz tptp.a)) (let ((_let_1 (@ X Xz))) (let ((_let_2 (and _let_1 (not _let_1)))) (or _let_2 _let_2)))) (lambda ((Xx tptp.a)) false)))))) (let ((_let_2 (forall ((BOUND_VARIABLE_618 tptp.a)) (not (ho_4 k_7 BOUND_VARIABLE_618))))) (let ((_let_3 (ho_4 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65))) (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_6 v ii) (ite (= i ii) e (ho_6 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_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_8 (forall ((BOUND_VARIABLE_647 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_624 tptp.a)) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_647) BOUND_VARIABLE_624))))) (let ((_let_9 (forall ((BOUND_VARIABLE_664 |u_(-> tptp.a Bool)|)) (= k_7 (ho_6 k_5 BOUND_VARIABLE_664))))) (let ((_let_10 (not _let_9))) (let ((_let_11 (forall ((BOUND_VARIABLE_623 (-> tptp.a Bool)) (BOUND_VARIABLE_624 tptp.a)) (not (ll_3 BOUND_VARIABLE_623 BOUND_VARIABLE_624))))) (let ((_let_12 (forall ((BOUND_VARIABLE_618 tptp.a)) (not (ll_2 BOUND_VARIABLE_618))))) (let ((_let_13 (not (forall ((X (-> tptp.a Bool))) (= ll_2 (@ ll_3 X)))))) (let ((_let_14 (and _let_13 _let_12 _let_11))) (let ((_let_15 (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))) (= (lambda ((Xz tptp.a)) (let ((_let_1 (@ X Xz))) (and _let_1 (not _let_1)))) (lambda ((BOUND_VARIABLE_598 tptp.a)) false)))) _let_13))))) (PREPROCESS :args ((and _let_12 _let_11)))) :args (_let_14)) (PREPROCESS :args ((= _let_14 (and _let_10 _let_2 _let_8))))) (PREPROCESS :args ((and _let_7 _let_6 _let_5 _let_4)))) :args ((and _let_10 _let_2 _let_8 _let_7 _let_6 _let_5 _let_4))))) (let ((_let_16 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_17 (ho_4 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65))) (let ((_let_18 (= _let_17 _let_3))) (let ((_let_19 (forall ((z tptp.a)) (= (ho_4 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) z) (ho_4 k_7 z))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (= k_7 _let_16))) (let ((_let_22 (not _let_19))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (_let_5))) (let ((_let_25 (not _let_21))) (let ((_let_26 (or))) (let ((_let_27 (_let_10))) (let ((_let_28 (_let_22))) (let ((_let_29 (_let_8))) (let ((_let_30 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_30) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_18)) :args ((or _let_17 _let_3 _let_18))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_29)) (AND_ELIM _let_15 :args (2)) :args ((not _let_17) false _let_8)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_28)) :args _let_28)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_19))) (REFL :args (_let_20)) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_21 _let_22 (not _let_23)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_27)) :args _let_27)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) (REFL :args (_let_25)) :args _let_26)) (AND_ELIM _let_15 :args (0)) :args (_let_25 true _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_24) :args (_let_16 k_7 QUANTIFIERS_INST_ENUM)) :args _let_24))) (AND_ELIM _let_15 :args (5)) :args (_let_23 false _let_5)) :args (_let_22 true _let_21 false _let_23)) :args (_let_20 true _let_19)) :args (_let_3 true _let_17 true _let_18)) (AND_ELIM _let_15 :args (1)) :args (false false _let_3 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))
% 0.20/0.56 )
% 0.20/0.56 % SZS output end Proof for SET618^5
% 0.20/0.56 % cvc5---1.0.5 exiting
% 0.20/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------