TSTP Solution File: PUZ137^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ137^1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 13:13:33 EDT 2023
% Result : Theorem 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ137^1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.18/0.36 % Computer : n022.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Sat Aug 26 22:07:40 EDT 2023
% 0.18/0.36 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 % File : PUZ137^1 : TPTP v8.1.2. Released v5.3.0.
% 0.22/0.54 % Domain : Puzzles
% 0.22/0.54 % Problem : Peter the liar says everything
% 0.22/0.54 % Version : Especial.
% 0.22/0.54 % English : Peter says that everything he says is false. Show that Peter says
% 0.22/0.54 % everything.
% 0.22/0.54
% 0.22/0.54 % Refs : [Bro11] Brown (2011), Email to G. Sutcliffe
% 0.22/0.54 % Source : [Bro11]
% 0.22/0.54 % Names :
% 0.22/0.54
% 0.22/0.54 % Status : Theorem
% 0.22/0.54 % Rating : 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.1.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.25 v5.3.0
% 0.22/0.54 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 0 def)
% 0.22/0.54 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.22/0.54 % Maximal formula atoms : 2 ( 1 avg)
% 0.22/0.54 % Number of connectives : 8 ( 1 ~; 0 |; 0 &; 6 @)
% 0.22/0.54 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.22/0.54 % Maximal formula depth : 6 ( 5 avg)
% 0.22/0.54 % Number of types : 2 ( 0 usr)
% 0.22/0.54 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.22/0.54 % Number of symbols : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.22/0.54 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.22/0.54 % SPC : TH0_THM_NEQ_NAR
% 0.22/0.54
% 0.22/0.54 % Comments : This is PUZ082^1 with a different conjecture. The idea of using
% 0.22/0.54 % truth values ($o) to interpret statements seems to go back to
% 0.22/0.54 % Frege. One criticism of this idea is that it can lead to
% 0.22/0.54 % unexpected consequences, often due to extensionality. In addition
% 0.22/0.54 % to being a theorem of extensional simple type theory, it's also
% 0.22/0.54 % an example of why assigning a type ($i > $o > $o) to a relation
% 0.22/0.54 % like 'says' may be dangerous.
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 %----Signature
% 0.22/0.54 thf(peter,type,
% 0.22/0.54 peter: $i ).
% 0.22/0.54
% 0.22/0.54 thf(says,type,
% 0.22/0.54 says: $i > $o > $o ).
% 0.22/0.54
% 0.22/0.54 %----Axioms
% 0.22/0.54 thf(ax1,axiom,
% 0.22/0.54 ( says @ peter
% 0.22/0.54 @ ! [X: $o] :
% 0.22/0.54 ( ( says @ peter @ X )
% 0.22/0.54 => ~ X ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(thm,conjecture,
% 0.22/0.54 ! [X: $o] : ( says @ peter @ X ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.x1jMsP9Mxy/cvc5---1.0.5_30372.p...
% 0.22/0.54 (declare-sort $$unsorted 0)
% 0.22/0.54 (declare-fun tptp.peter () $$unsorted)
% 0.22/0.54 (declare-fun tptp.says ($$unsorted Bool) Bool)
% 0.22/0.54 (assert (@ (@ tptp.says tptp.peter) (forall ((X Bool)) (=> (@ (@ tptp.says tptp.peter) X) (not X)))))
% 0.22/0.54 (assert (not (forall ((X Bool)) (@ (@ tptp.says tptp.peter) X))))
% 0.22/0.54 (set-info :filename cvc5---1.0.5_30372)
% 0.22/0.54 (check-sat-assuming ( true ))
% 0.22/0.54 ------- get file name : TPTP file name is PUZ137^1
% 0.22/0.54 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30372.smt2...
% 0.22/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.54 % SZS status Theorem for PUZ137^1
% 0.22/0.54 % SZS output start Proof for PUZ137^1
% 0.22/0.54 (
% 0.22/0.54 (let ((_let_1 (not (forall ((X Bool)) (@ (@ tptp.says tptp.peter) X))))) (let ((_let_2 (@ tptp.says tptp.peter))) (let ((_let_3 (@ _let_2 (forall ((X Bool)) (=> (@ (@ tptp.says tptp.peter) X) (not X)))))) (let ((_let_4 (ho_3 k_2 tptp.peter))) (let ((_let_5 (ho_4 _let_4 BOOLEAN_TERM_VARIABLE_698))) (let ((_let_6 (ho_4 _let_4 BOOLEAN_TERM_VARIABLE_836))) (let ((_let_7 (forall ((u |u_(-> Bool Bool)|) (e Bool) (i Bool)) (not (forall ((v |u_(-> Bool Bool)|)) (not (forall ((ii Bool)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_8 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_9 (forall ((u |u_(-> $$unsorted Bool Bool)|) (e |u_(-> Bool Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_10 (forall ((x |u_(-> $$unsorted Bool Bool)|) (y |u_(-> $$unsorted Bool Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_11 (APPLY_UF ho_4))) (let ((_let_12 (not (ho_4 _let_4 true)))) (let ((_let_13 (REFL :args (_let_4)))) (let ((_let_14 (ho_4 _let_4 _let_12))) (let ((_let_15 (AND_ELIM (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ _let_2 (not (@ _let_2 true))) _let_14))))) (PREPROCESS :args ((and _let_10 _let_9 _let_8 _let_7)))) :args ((and _let_14 _let_10 _let_9 _let_8 _let_7))) (CONG (CONG _let_13 (MACRO_SR_PRED_INTRO :args ((= _let_12 BOOLEAN_TERM_VARIABLE_698))) :args _let_11) (REFL :args (_let_10)) (REFL :args (_let_9)) (REFL :args (_let_8)) (REFL :args (_let_7)) :args (and))) :args (0)))) (let ((_let_16 (forall ((X Bool)) (ho_4 (ho_3 k_2 tptp.peter) X)))) (let ((_let_17 (not _let_6))) (let ((_let_18 (not _let_16))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_18)))))) (let ((_let_20 (or))) (let ((_let_21 (_let_17))) (let ((_let_22 (not))) (let ((_let_23 (_let_18))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_19) :args _let_23) (CONG (REFL :args _let_23) (CONG (CONG _let_13 (MACRO_SR_PRED_INTRO :args ((= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOOLEAN_TERM_VARIABLE_836))) :args _let_11) :args _let_22) :args (=>)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_16))) (REFL :args _let_21) :args _let_20)) _let_19 :args (_let_17 true _let_16)))) (let ((_let_25 (ho_4 _let_4 BOOLEAN_TERM_VARIABLE_707))) (let ((_let_26 (not BOOLEAN_TERM_VARIABLE_698))) (let ((_let_27 (not _let_25))) (let ((_let_28 (BOOLEAN_TERM_VARIABLE_698))) (let ((_let_29 (REFL :args _let_28))) (let ((_let_30 (MACRO_SR_PRED_INTRO :args ((= true BOOLEAN_TERM_VARIABLE_707))))) (let ((_let_31 ((= BOOLEAN_TERM_VARIABLE_698 _let_12)))) (let ((_let_32 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_31) (TRANS (REWRITE :args _let_31) (TRANS (CONG (CONG (CONG _let_13 _let_30 :args _let_11) :args _let_22) _let_29 :args (=)) (REWRITE :args ((= _let_27 BOOLEAN_TERM_VARIABLE_698)))))))) (let ((_let_33 ((= BOOLEAN_TERM_VARIABLE_707 true)))) (let ((_let_34 (MACRO_SR_PRED_INTRO :args _let_33))) (let ((_let_35 (EQ_RESOLVE _let_34 (REWRITE :args _let_33)))) (let ((_let_36 (not BOOLEAN_TERM_VARIABLE_707))) (let ((_let_37 (not _let_5))) (let ((_let_38 (and BOOLEAN_TERM_VARIABLE_698 _let_5 BOOLEAN_TERM_VARIABLE_707))) (let ((_let_39 (ASSUME :args (_let_5)))) (let ((_let_40 (TRUE_INTRO _let_39))) (let ((_let_41 (ASSUME :args _let_28))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_38)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_39 _let_41 _let_35) (SCOPE (TRUE_ELIM (TRANS (CONG _let_13 (TRANS _let_34 (SYMM (TRUE_INTRO _let_41))) :args _let_11) _let_40)) :args (_let_5 BOOLEAN_TERM_VARIABLE_698 BOOLEAN_TERM_VARIABLE_707))) :args (BOOLEAN_TERM_VARIABLE_698 _let_5 BOOLEAN_TERM_VARIABLE_707))) :args (true _let_38)) :args ((or _let_25 _let_37 _let_26 _let_36))) _let_35 _let_15 (REORDERING (EQUIV_ELIM1 _let_32) :args ((or _let_27 _let_26))) :args (_let_26 false BOOLEAN_TERM_VARIABLE_707 false _let_5 true _let_25)))) (let ((_let_43 (not BOOLEAN_TERM_VARIABLE_836))) (let ((_let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_6))))) (let ((_let_45 (_let_43))) (let ((_let_46 (ASSUME :args (_let_25)))) (let ((_let_47 (ASSUME :args (BOOLEAN_TERM_VARIABLE_836)))) (let ((_let_48 (ASSUME :args _let_21))) (let ((_let_49 (SYMM (FALSE_INTRO _let_48)))) (let ((_let_50 (ASSUME :args (_let_26)))) (let ((_let_51 (ASSUME :args _let_45))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_39 _let_50 _let_51 _let_48) :args (_let_5 _let_26 _let_17 _let_43)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_49 (CONG _let_13 (TRANS (FALSE_INTRO _let_51) (SYMM (FALSE_INTRO _let_50))) :args _let_11) _let_40)) :args (_let_5 _let_26 _let_43 _let_17)) :args ((not (and _let_5 _let_26 _let_17 _let_43)) SB_LITERAL))) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) BOOLEAN_TERM_VARIABLE_698))) _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) BOOLEAN_TERM_VARIABLE_836))) :args _let_20)) :args ((or BOOLEAN_TERM_VARIABLE_698 _let_37 BOOLEAN_TERM_VARIABLE_836 _let_6))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_46 _let_35 _let_47 _let_48) :args (BOOLEAN_TERM_VARIABLE_707 _let_25 BOOLEAN_TERM_VARIABLE_836 _let_17)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_49 (CONG _let_13 (TRANS (TRUE_INTRO _let_47) _let_30) :args _let_11) (TRUE_INTRO _let_46))) :args (_let_25 BOOLEAN_TERM_VARIABLE_707 BOOLEAN_TERM_VARIABLE_836 _let_17)) :args ((not (and BOOLEAN_TERM_VARIABLE_707 _let_25 BOOLEAN_TERM_VARIABLE_836 _let_17)) SB_LITERAL))) (CONG (REFL :args (_let_36)) (REFL :args (_let_27)) (REFL :args _let_45) _let_44 :args _let_20)) :args ((or _let_27 _let_36 _let_6 _let_43))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (EQUIV_ELIM2 _let_32) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_25))) :args _let_20)) _let_42 :args (_let_25 true BOOLEAN_TERM_VARIABLE_698)) _let_35 _let_24 :args (_let_43 false _let_25 false BOOLEAN_TERM_VARIABLE_707 true _let_6)) _let_42 _let_24 _let_15 :args (false true BOOLEAN_TERM_VARIABLE_836 true BOOLEAN_TERM_VARIABLE_698 true _let_6 false _let_5)) :args (_let_3 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.55 )
% 0.22/0.55 % SZS output end Proof for PUZ137^1
% 0.22/0.55 % cvc5---1.0.5 exiting
% 0.22/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------