TSTP Solution File: PUZ082^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ082^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 13:13:18 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ082^1 : TPTP v8.1.2. Released v3.6.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n024.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 22:40:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : PUZ082^1 : TPTP v8.1.2. Released v3.6.0.
% 0.21/0.53 % Domain : Puzzles
% 0.21/0.53 % Problem : Peter the liar
% 0.21/0.53 % Version : Especial.
% 0.21/0.53 % English : Peter says that everything he says is false. Show that not
% 0.21/0.53 % everything Peter says is false.
% 0.21/0.53
% 0.21/0.53 % Refs : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% 0.21/0.53 % Source : [Ben08]
% 0.21/0.53 % Names :
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % Rating : 0.09 v8.1.0, 0.00 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v4.1.0, 0.33 v3.7.0
% 0.21/0.53 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 0 def)
% 0.21/0.53 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 2 ( 1 avg)
% 0.21/0.53 % Number of connectives : 11 ( 3 ~; 0 |; 0 &; 6 @)
% 0.21/0.53 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 6 ( 6 avg)
% 0.21/0.53 % Number of types : 2 ( 0 usr)
% 0.21/0.53 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.21/0.53 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.21/0.53 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.53
% 0.21/0.53 % Comments :
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 %----Signature
% 0.21/0.53 thf(peter,type,
% 0.21/0.53 peter: $i ).
% 0.21/0.53
% 0.21/0.53 thf(says,type,
% 0.21/0.53 says: $i > $o > $o ).
% 0.21/0.53
% 0.21/0.53 %----Axioms
% 0.21/0.53 thf(ax1,axiom,
% 0.21/0.53 ( says @ peter
% 0.21/0.53 @ ! [X: $o] :
% 0.21/0.53 ( ( says @ peter @ X )
% 0.21/0.53 => ~ X ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(thm,conjecture,
% 0.21/0.53 ~ ! [X: $o] :
% 0.21/0.53 ( ( says @ peter @ X )
% 0.21/0.53 => ~ X ) ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wFEvRX0Hvt/cvc5---1.0.5_23960.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-fun tptp.peter () $$unsorted)
% 0.21/0.53 (declare-fun tptp.says ($$unsorted Bool) Bool)
% 0.21/0.53 (assert (@ (@ tptp.says tptp.peter) (forall ((X Bool)) (=> (@ (@ tptp.says tptp.peter) X) (not X)))))
% 0.21/0.53 (assert (not (not (forall ((X Bool)) (=> (@ (@ tptp.says tptp.peter) X) (not X))))))
% 0.21/0.53 (set-info :filename cvc5---1.0.5_23960)
% 0.21/0.53 (check-sat-assuming ( true ))
% 0.21/0.53 ------- get file name : TPTP file name is PUZ082^1
% 0.21/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23960.smt2...
% 0.21/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for PUZ082^1
% 0.21/0.53 % SZS output start Proof for PUZ082^1
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (not (not (forall ((X Bool)) (=> (@ (@ tptp.says tptp.peter) X) (not X))))))) (let ((_let_2 (@ tptp.says tptp.peter))) (let ((_let_3 (@ _let_2 (forall ((X Bool)) (=> (@ (@ tptp.says tptp.peter) X) (not X)))))) (let ((_let_4 (ho_3 k_2 tptp.peter))) (let ((_let_5 (ho_4 _let_4 BOOLEAN_TERM_VARIABLE_702))) (let ((_let_6 (ho_4 _let_4 BOOLEAN_TERM_VARIABLE_711))) (let ((_let_7 (forall ((u |u_(-> Bool Bool)|) (e Bool) (i Bool)) (not (forall ((v |u_(-> Bool Bool)|)) (not (forall ((ii Bool)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_8 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_9 (forall ((u |u_(-> $$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 (not (@ _let_2 true)))) (let ((_let_16 (CONG (CONG _let_13 (MACRO_SR_PRED_INTRO :args ((= true BOOLEAN_TERM_VARIABLE_711))) :args _let_11) :args (not)))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_15 _let_12))) _let_16)))) (let ((_let_18 (or))) (let ((_let_19 (not _let_6))) (let ((_let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_6))))) (let ((_let_21 (BOOLEAN_TERM_VARIABLE_702))) (let ((_let_22 (REFL :args _let_21))) (let ((_let_23 ((= BOOLEAN_TERM_VARIABLE_702 _let_12)))) (let ((_let_24 ((= BOOLEAN_TERM_VARIABLE_711 true)))) (let ((_let_25 (MACRO_SR_PRED_INTRO :args _let_24))) (let ((_let_26 (EQ_RESOLVE _let_25 (REWRITE :args _let_24)))) (let ((_let_27 (not BOOLEAN_TERM_VARIABLE_711))) (let ((_let_28 (not BOOLEAN_TERM_VARIABLE_702))) (let ((_let_29 (not _let_5))) (let ((_let_30 (ASSUME :args (_let_5)))) (let ((_let_31 (ASSUME :args _let_21))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_30 _let_31 _let_26 _let_17) :args (BOOLEAN_TERM_VARIABLE_702 _let_5 BOOLEAN_TERM_VARIABLE_711 _let_19)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_17)) (CONG _let_13 (TRANS _let_25 (SYMM (TRUE_INTRO _let_31))) :args _let_11) (TRUE_INTRO _let_30))) :args (_let_5 BOOLEAN_TERM_VARIABLE_702 BOOLEAN_TERM_VARIABLE_711 _let_19)) :args ((not (and BOOLEAN_TERM_VARIABLE_702 _let_5 BOOLEAN_TERM_VARIABLE_711 _let_19)) SB_LITERAL))) (CONG (REFL :args (_let_28)) (REFL :args (_let_29)) (REFL :args (_let_27)) _let_20 :args _let_18)) :args ((or _let_6 _let_29 _let_28 _let_27))) _let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (EQUIV_ELIM2 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_23) (TRANS (REWRITE :args _let_23) (TRANS (CONG _let_16 _let_22 :args (=)) (REWRITE :args ((= _let_19 BOOLEAN_TERM_VARIABLE_702))))))) (CONG _let_22 _let_20 :args _let_18)) _let_17 :args (BOOLEAN_TERM_VARIABLE_702 true _let_6)) _let_17 (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 _let_15) _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_702))) :args _let_11) (REFL :args (_let_10)) (REFL :args (_let_9)) (REFL :args (_let_8)) (REFL :args (_let_7)) :args (and))) :args (0)) :args (false false BOOLEAN_TERM_VARIABLE_711 false BOOLEAN_TERM_VARIABLE_702 true _let_6 false _let_5)) :args (_let_3 _let_1 true))))))))))))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for PUZ082^1
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------