TSTP Solution File: NUM707^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM707^1 : TPTP v8.1.2. Released v3.7.0.
% 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 10:47:06 EDT 2023
% Result : Theorem 0.16s 0.46s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM707^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 09:41:58 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.43 %----Proving TH0
% 0.16/0.46 %------------------------------------------------------------------------------
% 0.16/0.46 % File : NUM707^1 : TPTP v8.1.2. Released v3.7.0.
% 0.16/0.46 % Domain : Number Theory
% 0.16/0.46 % Problem : Landau theorem 28f
% 0.16/0.46 % Version : Especial.
% 0.16/0.46 % English : pl (ts x y) x = ts x (suc y)
% 0.16/0.46
% 0.16/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.16/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.16/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.46 % Source : [Bro09]
% 0.16/0.46 % Names : satz28f [Lan30]
% 0.16/0.46
% 0.16/0.46 % Status : Theorem
% 0.16/0.46 % : Without extensionality : Theorem
% 0.16/0.46 % Rating : 0.00 v6.0.0, 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 v3.7.0
% 0.16/0.46 % Syntax : Number of formulae : 8 ( 2 unt; 6 typ; 0 def)
% 0.16/0.46 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.16/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.46 % Number of connectives : 14 ( 0 ~; 0 |; 0 &; 14 @)
% 0.16/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.46 % Maximal formula depth : 3 ( 2 avg)
% 0.16/0.46 % Number of types : 1 ( 1 usr)
% 0.16/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.16/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.16/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.16/0.46 % SPC : TH0_THM_EQU_NAR
% 0.16/0.46
% 0.16/0.46 % Comments :
% 0.16/0.46 %------------------------------------------------------------------------------
% 0.16/0.46 thf(nat_type,type,
% 0.16/0.46 nat: $tType ).
% 0.16/0.46
% 0.16/0.46 thf(x,type,
% 0.16/0.46 x: nat ).
% 0.16/0.46
% 0.16/0.46 thf(y,type,
% 0.16/0.46 y: nat ).
% 0.16/0.46
% 0.16/0.46 thf(pl,type,
% 0.16/0.46 pl: nat > nat > nat ).
% 0.16/0.46
% 0.16/0.46 thf(ts,type,
% 0.16/0.46 ts: nat > nat > nat ).
% 0.16/0.46
% 0.16/0.46 thf(suc,type,
% 0.16/0.46 suc: nat > nat ).
% 0.16/0.46
% 0.16/0.46 thf(satz28b,axiom,
% 0.16/0.46 ! [Xx: nat,Xy: nat] :
% 0.16/0.46 ( ( ts @ Xx @ ( suc @ Xy ) )
% 0.16/0.46 = ( pl @ ( ts @ Xx @ Xy ) @ Xx ) ) ).
% 0.16/0.46
% 0.16/0.46 thf(satz28f,conjecture,
% 0.16/0.46 ( ( pl @ ( ts @ x @ y ) @ x )
% 0.16/0.46 = ( ts @ x @ ( suc @ y ) ) ) ).
% 0.16/0.46
% 0.16/0.46 %------------------------------------------------------------------------------
% 0.16/0.46 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.gJI5iP5piZ/cvc5---1.0.5_2964.p...
% 0.16/0.46 (declare-sort $$unsorted 0)
% 0.16/0.46 (declare-sort tptp.nat 0)
% 0.16/0.46 (declare-fun tptp.x () tptp.nat)
% 0.16/0.46 (declare-fun tptp.y () tptp.nat)
% 0.16/0.46 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.16/0.46 (declare-fun tptp.ts (tptp.nat tptp.nat) tptp.nat)
% 0.16/0.46 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.16/0.46 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (let ((_let_1 (@ tptp.ts Xx))) (= (@ _let_1 (@ tptp.suc Xy)) (@ (@ tptp.pl (@ _let_1 Xy)) Xx)))))
% 0.16/0.46 (assert (let ((_let_1 (@ tptp.ts tptp.x))) (not (= (@ (@ tptp.pl (@ _let_1 tptp.y)) tptp.x) (@ _let_1 (@ tptp.suc tptp.y))))))
% 0.16/0.46 (set-info :filename cvc5---1.0.5_2964)
% 0.16/0.46 (check-sat-assuming ( true ))
% 0.16/0.46 ------- get file name : TPTP file name is NUM707^1
% 0.16/0.46 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2964.smt2...
% 0.16/0.46 --- Run --ho-elim --full-saturate-quant at 10...
% 0.16/0.46 % SZS status Theorem for NUM707^1
% 0.16/0.46 % SZS output start Proof for NUM707^1
% 0.16/0.46 (
% 0.16/0.46 (let ((_let_1 (@ tptp.ts tptp.x))) (let ((_let_2 (not (= (@ (@ tptp.pl (@ _let_1 tptp.y)) tptp.x) (@ _let_1 (@ tptp.suc tptp.y)))))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat)) (let ((_let_1 (@ tptp.ts Xx))) (= (@ _let_1 (@ tptp.suc Xy)) (@ (@ tptp.pl (@ _let_1 Xy)) Xx)))))) (let ((_let_4 (forall ((Xx tptp.nat) (Xy tptp.nat)) (let ((_let_1 (ho_3 k_2 Xx))) (= (ho_4 (ho_3 k_5 (ho_4 _let_1 Xy)) Xx) (ho_4 _let_1 (ho_4 k_6 Xy))))))) (let ((_let_5 (ho_3 k_2 tptp.x))) (let ((_let_6 (= (ho_4 _let_5 (ho_4 k_6 tptp.y)) (ho_4 (ho_3 k_5 (ho_4 _let_5 tptp.y)) tptp.x)))) (let ((_let_7 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_8 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_9 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_10 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_11 (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_4)))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_11 :args (tptp.x tptp.y QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_4)))) :args ((or _let_6 (not _let_4)))) (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 (not _let_6))))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_11 (PREPROCESS :args ((and _let_10 _let_9 _let_8 _let_7)))) :args ((and _let_4 _let_10 _let_9 _let_8 _let_7))) :args (0)) :args (false true _let_6 false _let_4)) :args (_let_3 _let_2 true))))))))))))))
% 0.16/0.47 )
% 0.16/0.47 % SZS output end Proof for NUM707^1
% 0.16/0.47 % cvc5---1.0.5 exiting
% 0.16/0.47 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------