TSTP Solution File: SET612^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET612^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 14:39:28 EDT 2023
% Result : Theorem 0.22s 0.71s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET612^5 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 15:49:38 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.71 %------------------------------------------------------------------------------
% 0.22/0.71 % File : SET612^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.71 % Domain : Set Theory
% 0.22/0.71 % Problem : TPS problem BOOL-PROP-85
% 0.22/0.71 % Version : Especial.
% 0.22/0.71 % English : Trybulec's 85th Boolean property of sets
% 0.22/0.71
% 0.22/0.71 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.22/0.71 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.71 % Source : [Bro09]
% 0.22/0.71 % Names : tps_0309 [Bro09]
% 0.22/0.71 % : BOOL-PROP-85 [TPS]
% 0.22/0.71
% 0.22/0.71 % Status : Theorem
% 0.22/0.71 % 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, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.22/0.71 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.22/0.71 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.22/0.71 % Maximal formula atoms : 1 ( 1 avg)
% 0.22/0.71 % Number of connectives : 15 ( 3 ~; 1 |; 4 &; 7 @)
% 0.22/0.71 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.22/0.71 % Maximal formula depth : 4 ( 4 avg)
% 0.22/0.71 % Number of types : 2 ( 1 usr)
% 0.22/0.71 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.22/0.71 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.22/0.71 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.22/0.71 % SPC : TH0_THM_EQU_NAR
% 0.22/0.71
% 0.22/0.71 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.71 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.71 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.71 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.71 % : Polymorphic definitions expanded.
% 0.22/0.71 %------------------------------------------------------------------------------
% 0.22/0.71 thf(a_type,type,
% 0.22/0.71 a: $tType ).
% 0.22/0.71
% 0.22/0.71 thf(cBOOL_PROP_85_pme,conjecture,
% 0.22/0.71 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.22/0.71 ( ( ^ [Xx: a] :
% 0.22/0.71 ( ( X @ Xx )
% 0.22/0.71 & ~ ( ( Y @ Xx )
% 0.22/0.71 | ( Z @ Xx ) ) ) )
% 0.22/0.71 = ( ^ [Xx: a] :
% 0.22/0.71 ( ( X @ Xx )
% 0.22/0.71 & ~ ( Y @ Xx )
% 0.22/0.71 & ( X @ Xx )
% 0.22/0.71 & ~ ( Z @ Xx ) ) ) ) ).
% 0.22/0.71
% 0.22/0.71 %------------------------------------------------------------------------------
% 0.22/0.71 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.fxBRyL5nwy/cvc5---1.0.5_4609.p...
% 0.22/0.71 (declare-sort $$unsorted 0)
% 0.22/0.71 (declare-sort tptp.a 0)
% 0.22/0.71 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (= (lambda ((Xx tptp.a)) (and (@ X Xx) (not (or (@ Y Xx) (@ Z Xx))))) (lambda ((Xx tptp.a)) (let ((_let_1 (@ X Xx))) (and _let_1 (not (@ Y Xx)) _let_1 (not (@ Z Xx)))))))))
% 0.22/0.71 (set-info :filename cvc5---1.0.5_4609)
% 0.22/0.71 (check-sat-assuming ( true ))
% 0.22/0.71 ------- get file name : TPTP file name is SET612^5
% 0.22/0.71 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4609.smt2...
% 0.22/0.71 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.71 % SZS status Theorem for SET612^5
% 0.22/0.71 % SZS output start Proof for SET612^5
% 0.22/0.71 (
% 0.22/0.71 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (= (lambda ((Xx tptp.a)) (and (@ X Xx) (not (or (@ Y Xx) (@ Z Xx))))) (lambda ((Xx tptp.a)) (let ((_let_1 (@ X Xx))) (and _let_1 (not (@ Y Xx)) _let_1 (not (@ Z Xx)))))))))) (let ((_let_2 (and (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301) (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301)) (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301))))) (let ((_let_3 (ho_8 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_4 (ho_4 _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301))) (let ((_let_5 (= _let_4 _let_2))) (let ((_let_6 (forall ((BOUND_VARIABLE_698 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_695 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_690 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_657 tptp.a)) (= (and (ho_4 BOUND_VARIABLE_698 BOUND_VARIABLE_657) (not (ho_4 BOUND_VARIABLE_695 BOUND_VARIABLE_657)) (not (ho_4 BOUND_VARIABLE_690 BOUND_VARIABLE_657))) (ho_4 (ho_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_698) BOUND_VARIABLE_695) BOUND_VARIABLE_690) BOUND_VARIABLE_657))))) (let ((_let_7 (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_8 (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_9 (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_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_10 (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_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_11 (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_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_12 (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_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_13 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ _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_14 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ _u_(-> tptp.a Bool)_ tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ _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_15 (forall ((BOUND_VARIABLE_727 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_730 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_724 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_643 tptp.a)) (= (and (ho_4 BOUND_VARIABLE_730 BOUND_VARIABLE_643) (not (ho_4 BOUND_VARIABLE_727 BOUND_VARIABLE_643)) (not (ho_4 BOUND_VARIABLE_724 BOUND_VARIABLE_643))) (ho_4 (ho_8 (ho_7 (ho_6 k_9 BOUND_VARIABLE_727) BOUND_VARIABLE_730) BOUND_VARIABLE_724) BOUND_VARIABLE_643))))) (let ((_let_16 (forall ((BOUND_VARIABLE_747 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_746 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_745 |u_(-> tptp.a Bool)|)) (= (ho_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_747) BOUND_VARIABLE_746) BOUND_VARIABLE_745) (ho_8 (ho_7 (ho_6 k_9 BOUND_VARIABLE_746) BOUND_VARIABLE_747) BOUND_VARIABLE_745))))) (let ((_let_17 (not _let_16))) (let ((_let_18 (forall ((BOUND_VARIABLE_654 (-> tptp.a Bool)) (BOUND_VARIABLE_655 (-> tptp.a Bool)) (BOUND_VARIABLE_656 (-> tptp.a Bool)) (BOUND_VARIABLE_657 tptp.a)) (= (ll_3 BOUND_VARIABLE_654 BOUND_VARIABLE_655 BOUND_VARIABLE_656 BOUND_VARIABLE_657) (and (@ BOUND_VARIABLE_654 BOUND_VARIABLE_657) (not (@ BOUND_VARIABLE_655 BOUND_VARIABLE_657)) (not (@ BOUND_VARIABLE_656 BOUND_VARIABLE_657))))))) (let ((_let_19 (forall ((BOUND_VARIABLE_640 (-> tptp.a Bool)) (BOUND_VARIABLE_641 (-> tptp.a Bool)) (BOUND_VARIABLE_642 (-> tptp.a Bool)) (BOUND_VARIABLE_643 tptp.a)) (= (ll_2 BOUND_VARIABLE_640 BOUND_VARIABLE_641 BOUND_VARIABLE_642 BOUND_VARIABLE_643) (and (@ BOUND_VARIABLE_641 BOUND_VARIABLE_643) (not (@ BOUND_VARIABLE_640 BOUND_VARIABLE_643)) (not (@ BOUND_VARIABLE_642 BOUND_VARIABLE_643))))))) (let ((_let_20 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (= (@ (@ (@ ll_2 Y) X) Z) (@ (@ (@ ll_3 X) Y) Z)))))) (let ((_let_21 (and _let_20 _let_19 _let_18))) (let ((_let_22 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_20)))) (PREPROCESS :args ((and _let_19 _let_18)))) :args (_let_21)) (PREPROCESS :args ((= _let_21 (and _let_17 _let_15 _let_6))))) (PREPROCESS :args ((and _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7)))) :args ((and _let_17 _let_15 _let_6 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7))))) (let ((_let_23 (_let_6))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_23) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301 QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_698) BOUND_VARIABLE_695) BOUND_VARIABLE_690) BOUND_VARIABLE_657)))) :args _let_23))) (AND_ELIM _let_22 :args (2)) :args (_let_5 false _let_6)))) (let ((_let_25 (ho_8 (ho_7 (ho_6 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_26 (ho_4 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301))) (let ((_let_27 (= _let_26 _let_4))) (let ((_let_28 (forall ((z tptp.a)) (= (ho_4 (ho_8 (ho_7 (ho_6 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) z) (ho_4 (ho_8 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) z))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (= _let_3 _let_25))) (let ((_let_31 (not _let_28))) (let ((_let_32 (or _let_31 _let_30))) (let ((_let_33 (_let_8))) (let ((_let_34 (not _let_30))) (let ((_let_35 (or))) (let ((_let_36 (_let_17))) (let ((_let_37 (_let_31))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_37)) :args _let_37)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_28))) (REFL :args (_let_29)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_30 _let_31 (not _let_32)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_36)) :args _let_36)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) (REFL :args (_let_34)) :args _let_35)) (AND_ELIM _let_22 :args (0)) :args (_let_34 true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (_let_25 _let_3 QUANTIFIERS_INST_ENUM)) :args _let_33))) (AND_ELIM _let_22 :args (9)) :args (_let_32 false _let_8)) :args (_let_31 true _let_30 false _let_32)) :args (_let_29 true _let_28)))) (let ((_let_39 (= _let_26 _let_2))) (let ((_let_40 (not _let_26))) (let ((_let_41 (_let_27))) (let ((_let_42 (_let_15))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301 QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_8 (ho_7 (ho_6 k_9 BOUND_VARIABLE_727) BOUND_VARIABLE_730) BOUND_VARIABLE_724) BOUND_VARIABLE_643)))) :args _let_42))) (AND_ELIM _let_22 :args (1)) :args (_let_39 false _let_15)))) (let ((_let_44 (not _let_39))) (let ((_let_45 (_let_39))) (let ((_let_46 (not _let_5))) (let ((_let_47 (not _let_2))) (let ((_let_48 (_let_5))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_48) :args ((or _let_4 _let_47 _let_46))) _let_24 (REORDERING (CNF_EQUIV_POS1 :args _let_45) :args ((or _let_40 _let_2 _let_44))) _let_43 (CNF_EQUIV_NEG2 :args _let_41) _let_38 :args (_let_40 false _let_5 false _let_2 false _let_39 true _let_4 true _let_27)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_48) :args ((or (not _let_4) _let_2 _let_46))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_45) :args ((or _let_26 _let_47 _let_44))) _let_49 _let_43 :args (_let_47 true _let_26 false _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_41) :args ((or _let_26 _let_4 _let_27))) _let_49 _let_38 :args (_let_4 true _let_26 true _let_27)) _let_24 :args (false true _let_2 false _let_4 false _let_5)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.71 )
% 0.22/0.71 % SZS output end Proof for SET612^5
% 0.22/0.71 % cvc5---1.0.5 exiting
% 0.22/0.71 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------