TSTP Solution File: NUM654^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM654^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 10:46:13 EDT 2023
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM654^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.17/0.34 % Computer : n012.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Fri Aug 25 15:40:11 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 % File : NUM654^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.52 % Domain : Number Theory
% 0.20/0.52 % Problem : Landau theorem 10e
% 0.20/0.52 % Version : Especial.
% 0.20/0.52 % English : ~(less x y) -> x = y
% 0.20/0.52
% 0.20/0.52 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.52 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.52 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.52 % Source : [Bro09]
% 0.20/0.52 % Names : satz10e [Lan30]
% 0.20/0.52
% 0.20/0.52 % Status : Theorem
% 0.20/0.52 % : Without extensionality : Theorem
% 0.20/0.52 % Rating : 0.15 v8.1.0, 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
% 0.20/0.52 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.20/0.52 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.20/0.52 % Maximal formula atoms : 3 ( 1 avg)
% 0.20/0.52 % Number of connectives : 18 ( 6 ~; 0 |; 0 &; 8 @)
% 0.20/0.52 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.52 % Maximal formula depth : 8 ( 6 avg)
% 0.20/0.52 % Number of types : 2 ( 1 usr)
% 0.20/0.52 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.52 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.20/0.52 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.20/0.52 % SPC : TH0_THM_EQU_NAR
% 0.20/0.52
% 0.20/0.52 % Comments :
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 thf(nat_type,type,
% 0.20/0.52 nat: $tType ).
% 0.20/0.52
% 0.20/0.52 thf(x,type,
% 0.20/0.52 x: nat ).
% 0.20/0.52
% 0.20/0.52 thf(y,type,
% 0.20/0.52 y: nat ).
% 0.20/0.52
% 0.20/0.52 thf(more,type,
% 0.20/0.52 more: nat > nat > $o ).
% 0.20/0.52
% 0.20/0.52 thf(n,axiom,
% 0.20/0.52 ~ ( more @ x @ y ) ).
% 0.20/0.52
% 0.20/0.52 thf(less,type,
% 0.20/0.52 less: nat > nat > $o ).
% 0.20/0.52
% 0.20/0.52 thf(et,axiom,
% 0.20/0.52 ! [Xa: $o] :
% 0.20/0.52 ( ~ ~ Xa
% 0.20/0.52 => Xa ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz10a,axiom,
% 0.20/0.52 ! [Xx: nat,Xy: nat] :
% 0.20/0.52 ( ( Xx != Xy )
% 0.20/0.52 => ( ~ ( more @ Xx @ Xy )
% 0.20/0.52 => ( less @ Xx @ Xy ) ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz10e,conjecture,
% 0.20/0.52 ( ~ ( less @ x @ y )
% 0.20/0.52 => ( x = y ) ) ).
% 0.20/0.52
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.CLvh9WgoLR/cvc5---1.0.5_29222.p...
% 0.20/0.52 (declare-sort $$unsorted 0)
% 0.20/0.52 (declare-sort tptp.nat 0)
% 0.20/0.52 (declare-fun tptp.x () tptp.nat)
% 0.20/0.52 (declare-fun tptp.y () tptp.nat)
% 0.20/0.52 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.20/0.52 (assert (not (@ (@ tptp.more tptp.x) tptp.y)))
% 0.20/0.52 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.20/0.52 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.20/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (not (= Xx Xy)) (=> (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.less Xx) Xy)))))
% 0.20/0.52 (assert (not (=> (not (@ (@ tptp.less tptp.x) tptp.y)) (= tptp.x tptp.y))))
% 0.20/0.52 (set-info :filename cvc5---1.0.5_29222)
% 0.20/0.52 (check-sat-assuming ( true ))
% 0.20/0.52 ------- get file name : TPTP file name is NUM654^1
% 0.20/0.52 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29222.smt2...
% 0.20/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.52 % SZS status Theorem for NUM654^1
% 0.20/0.52 % SZS output start Proof for NUM654^1
% 0.20/0.52 (
% 0.20/0.52 (let ((_let_1 (= tptp.x tptp.y))) (let ((_let_2 (not (=> (not (@ (@ tptp.less tptp.x) tptp.y)) _let_1)))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (not (= Xx Xy)) (=> (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.less Xx) Xy)))))) (let ((_let_4 (not (@ (@ tptp.more tptp.x) tptp.y)))) (let ((_let_5 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (= Xx Xy) (ho_4 (ho_3 k_2 Xx) Xy) (ho_4 (ho_3 k_5 Xx) Xy))))) (let ((_let_6 (ho_4 (ho_3 k_5 tptp.x) tptp.y))) (let ((_let_7 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_8 (or _let_1 _let_7 _let_6))) (let ((_let_9 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (= Xx Xy) (@ (@ tptp.more Xx) Xy) (@ (@ tptp.less Xx) Xy))) _let_5))))))) (let ((_let_10 (not _let_8))) (let ((_let_11 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 (not (=> (not _let_6) _let_1)))))))) (let ((_let_12 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_13 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_14 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_15 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_16 (not _let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (tptp.x tptp.y QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_5))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_1 _let_7 _let_6 _let_10))) (NOT_IMPLIES_ELIM2 _let_11) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_16)))) (PREPROCESS :args ((and _let_15 _let_14 _let_13 _let_12)))) :args ((and _let_16 _let_15 _let_14 _let_13 _let_12))) :args (0)) (NOT_IMPLIES_ELIM1 _let_11) :args (_let_10 true _let_1 true _let_7 true _let_6)) _let_9 :args (false true _let_8 false _let_5)) :args (_let_4 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_3 _let_2 true)))))))))))))))))))
% 0.20/0.52 )
% 0.20/0.52 % SZS output end Proof for NUM654^1
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------