TSTP Solution File: SET183^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET183^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 14:38:06 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET183^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 16:54:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.61 %------------------------------------------------------------------------------
% 0.21/0.61 % File : SET183^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.61 % Domain : Set Theory
% 0.21/0.61 % Problem : TPS problem BOOL-PROP-42
% 0.21/0.61 % Version : Especial.
% 0.21/0.61 % English : Trybulec's 42nd Boolean property of sets
% 0.21/0.61
% 0.21/0.61 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.21/0.61 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.61 % Source : [Bro09]
% 0.21/0.61 % Names : tps_0109 [Bro09]
% 0.21/0.61 % : BOOL-PROP-42 [TPS]
% 0.21/0.61
% 0.21/0.61 % Status : Theorem
% 0.21/0.61 % 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 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.21/0.61 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.21/0.61 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.21/0.61 % Maximal formula atoms : 1 ( 1 avg)
% 0.21/0.61 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.21/0.61 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.61 % Maximal formula depth : 7 ( 7 avg)
% 0.21/0.61 % Number of types : 2 ( 1 usr)
% 0.21/0.61 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.61 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.61 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.21/0.61 % SPC : TH0_THM_EQU_NAR
% 0.21/0.61
% 0.21/0.61 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.61 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.61 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.61 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.61 % : Polymorphic definitions expanded.
% 0.21/0.61 % :
% 0.21/0.61 %------------------------------------------------------------------------------
% 0.21/0.61 thf(a_type,type,
% 0.21/0.61 a: $tType ).
% 0.21/0.61
% 0.21/0.61 thf(cBOOL_PROP_42_pme,conjecture,
% 0.21/0.61 ! [X: a > $o,Y: a > $o] :
% 0.21/0.61 ( ! [Xx: a] :
% 0.21/0.61 ( ( X @ Xx )
% 0.21/0.61 => ( Y @ Xx ) )
% 0.21/0.61 => ( ( ^ [Xx: a] :
% 0.21/0.61 ( ( X @ Xx )
% 0.21/0.61 & ( Y @ Xx ) ) )
% 0.21/0.61 = X ) ) ).
% 0.21/0.61
% 0.21/0.61 %------------------------------------------------------------------------------
% 0.21/0.61 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.kjgISmLkhb/cvc5---1.0.5_10816.p...
% 0.21/0.61 (declare-sort $$unsorted 0)
% 0.21/0.61 (declare-sort tptp.a 0)
% 0.21/0.61 (assert (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (= (lambda ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))) X)))))
% 0.21/0.61 (set-info :filename cvc5---1.0.5_10816)
% 0.21/0.61 (check-sat-assuming ( true ))
% 0.21/0.61 ------- get file name : TPTP file name is SET183^5
% 0.21/0.61 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10816.smt2...
% 0.21/0.61 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.61 % SZS status Theorem for SET183^5
% 0.21/0.61 % SZS output start Proof for SET183^5
% 0.21/0.61 (
% 0.21/0.61 (let ((_let_1 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (=> (forall ((Xx tptp.a)) (=> (@ X Xx) (@ Y Xx))) (= (lambda ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))) X)))))) (let ((_let_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90))) (let ((_let_3 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90))) (let ((_let_4 (and _let_3 _let_2))) (let ((_let_5 (ho_6 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_6 (ho_3 _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90))) (let ((_let_7 (= _let_6 _let_4))) (let ((_let_8 (forall ((BOUND_VARIABLE_641 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_638 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_623 tptp.a)) (= (ho_3 (ho_6 (ho_5 k_4 BOUND_VARIABLE_641) BOUND_VARIABLE_638) BOUND_VARIABLE_623) (and (ho_3 BOUND_VARIABLE_641 BOUND_VARIABLE_623) (ho_3 BOUND_VARIABLE_638 BOUND_VARIABLE_623)))))) (let ((_let_9 (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_10 (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_11 (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_12 (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_13 (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_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_14 (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_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_15 (forall ((BOUND_VARIABLE_660 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_659 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xx tptp.a)) (or (not (ho_3 BOUND_VARIABLE_660 Xx)) (ho_3 BOUND_VARIABLE_659 Xx)))) (= BOUND_VARIABLE_660 (ho_6 (ho_5 k_4 BOUND_VARIABLE_660) BOUND_VARIABLE_659)))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((BOUND_VARIABLE_621 (-> tptp.a Bool)) (BOUND_VARIABLE_622 (-> tptp.a Bool)) (BOUND_VARIABLE_623 tptp.a)) (= (and (@ BOUND_VARIABLE_621 BOUND_VARIABLE_623) (@ BOUND_VARIABLE_622 BOUND_VARIABLE_623)) (ll_2 BOUND_VARIABLE_621 BOUND_VARIABLE_622 BOUND_VARIABLE_623))))) (let ((_let_18 (not (forall ((X (-> tptp.a Bool)) (Y (-> tptp.a Bool))) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (= X (@ (@ ll_2 X) Y))))))) (let ((_let_19 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (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))) (or (not (forall ((Xx tptp.a)) (or (not (@ X Xx)) (@ Y Xx)))) (= X (lambda ((Xx tptp.a)) (and (@ X Xx) (@ Y Xx))))))) _let_18))))) (PREPROCESS :args (_let_17))) (PREPROCESS :args ((= (and _let_18 _let_17) (and _let_16 _let_8))))) (PREPROCESS :args ((and _let_14 _let_13 _let_12 _let_11 _let_10 _let_9)))) :args ((and _let_16 _let_8 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9))))) (let ((_let_20 (_let_8))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_20) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 QUANTIFIERS_INST_E_MATCHING ((ho_3 (ho_6 (ho_5 k_4 BOUND_VARIABLE_641) BOUND_VARIABLE_638) BOUND_VARIABLE_623)))) :args _let_20)) (AND_ELIM _let_19 :args (1)) :args (_let_7 false _let_8)))) (let ((_let_22 (= _let_3 _let_6))) (let ((_let_23 (forall ((z tptp.a)) (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 z) (ho_3 (ho_6 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) z))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_5))) (let ((_let_26 (not _let_23))) (let ((_let_27 (or _let_26 _let_25))) (let ((_let_28 (_let_10))) (let ((_let_29 (forall ((Xx tptp.a)) (or (not (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx)) (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_25))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or))) (let ((_let_34 (_let_16))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_34)) :args _let_34)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) (REFL :args (_let_32)) :args _let_33)) (AND_ELIM _let_19 :args (0)) :args (_let_32 true _let_15)))) (let ((_let_36 (_let_26))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_36)) :args _let_36)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_23))) (REFL :args (_let_24)) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_25 _let_26 (not _let_27)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 1)) _let_35 :args ((not _let_25) true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_28) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_5 QUANTIFIERS_INST_ENUM)) :args _let_28)) (AND_ELIM _let_19 :args (6)) :args (_let_27 false _let_10)) :args (_let_26 true _let_25 false _let_27)) :args (_let_24 true _let_23)))) (let ((_let_38 (not _let_3))) (let ((_let_39 (or _let_38 _let_2))) (let ((_let_40 (_let_22))) (let ((_let_41 (_let_29))) (let ((_let_42 (not _let_7))) (let ((_let_43 (not _let_4))) (let ((_let_44 (_let_7))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_4)) :args ((or _let_38 _let_4 (not _let_2)))) (REORDERING (CNF_EQUIV_POS2 :args _let_44) :args ((or _let_6 _let_43 _let_42))) _let_21 (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_2 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx) false))))) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG (REFL :args (_let_31)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_33)) :args ((or _let_29 _let_31))) _let_35 :args (_let_29 true _let_31)) :args (_let_39 false _let_29)) (CNF_EQUIV_NEG2 :args _let_40) _let_37 :args (_let_38 true _let_4 false _let_7 false _let_2 false _let_39 true _let_6 true _let_22)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_44) :args ((or (not _let_6) _let_4 _let_42))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_4 0)) :args ((or _let_3 _let_43))) _let_45 :args (_let_43 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_40) :args ((or _let_3 _let_6 _let_22))) _let_45 _let_37 :args (_let_6 true _let_3 true _let_22)) _let_21 :args (false true _let_4 false _let_6 false _let_7)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.61 )
% 0.21/0.61 % SZS output end Proof for SET183^5
% 0.21/0.62 % cvc5---1.0.5 exiting
% 0.21/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------