TSTP Solution File: NUM664^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM664^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 10:46:25 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 : NUM664^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 11:49:55 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : NUM664^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.53 % Domain : Number Theory
% 0.21/0.53 % Problem : Landau theorem 16b
% 0.21/0.53 % Version : Especial.
% 0.21/0.53 % English : less x z
% 0.21/0.53
% 0.21/0.53 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.53 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.53 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.53 % Source : [Bro09]
% 0.21/0.53 % Names : satz16b [Lan30]
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % : Without extensionality : Theorem
% 0.21/0.53 % Rating : 0.15 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 v3.7.0
% 0.21/0.53 % Syntax : Number of formulae : 10 ( 2 unt; 5 typ; 0 def)
% 0.21/0.53 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.53 % Number of connectives : 19 ( 3 ~; 0 |; 0 &; 12 @)
% 0.21/0.53 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 8 ( 5 avg)
% 0.21/0.53 % Number of types : 2 ( 1 usr)
% 0.21/0.53 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.21/0.53 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.21/0.53 % SPC : TH0_THM_EQU_NAR
% 0.21/0.53
% 0.21/0.53 % Comments :
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 thf(nat_type,type,
% 0.21/0.53 nat: $tType ).
% 0.21/0.53
% 0.21/0.53 thf(x,type,
% 0.21/0.53 x: nat ).
% 0.21/0.53
% 0.21/0.53 thf(y,type,
% 0.21/0.53 y: nat ).
% 0.21/0.53
% 0.21/0.53 thf(z,type,
% 0.21/0.53 z: nat ).
% 0.21/0.53
% 0.21/0.53 thf(less,type,
% 0.21/0.53 less: nat > nat > $o ).
% 0.21/0.53
% 0.21/0.53 thf(l,axiom,
% 0.21/0.53 less @ x @ y ).
% 0.21/0.53
% 0.21/0.53 thf(k,axiom,
% 0.21/0.53 ( ~ ( less @ y @ z )
% 0.21/0.53 => ( y = z ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(et,axiom,
% 0.21/0.53 ! [Xa: $o] :
% 0.21/0.53 ( ~ ~ Xa
% 0.21/0.53 => Xa ) ).
% 0.21/0.53
% 0.21/0.53 thf(satz15,axiom,
% 0.21/0.53 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.21/0.53 ( ( less @ Xx @ Xy )
% 0.21/0.53 => ( ( less @ Xy @ Xz )
% 0.21/0.53 => ( less @ Xx @ Xz ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(satz16b,conjecture,
% 0.21/0.53 less @ x @ z ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.jXRE8t4RB7/cvc5---1.0.5_12259.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-sort tptp.nat 0)
% 0.21/0.53 (declare-fun tptp.x () tptp.nat)
% 0.21/0.53 (declare-fun tptp.y () tptp.nat)
% 0.21/0.53 (declare-fun tptp.z () tptp.nat)
% 0.21/0.53 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.21/0.53 (assert (@ (@ tptp.less tptp.x) tptp.y))
% 0.21/0.53 (assert (=> (not (@ (@ tptp.less tptp.y) tptp.z)) (= tptp.y tptp.z)))
% 0.21/0.53 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.21/0.53 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (let ((_let_1 (@ tptp.less Xx))) (=> (@ _let_1 Xy) (=> (@ (@ tptp.less Xy) Xz) (@ _let_1 Xz))))))
% 0.21/0.53 (assert (not (@ (@ tptp.less tptp.x) tptp.z)))
% 0.21/0.53 (set-info :filename cvc5---1.0.5_12259)
% 0.21/0.53 (check-sat-assuming ( true ))
% 0.21/0.53 ------- get file name : TPTP file name is NUM664^1
% 0.21/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12259.smt2...
% 0.21/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for NUM664^1
% 0.21/0.53 % SZS output start Proof for NUM664^1
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (@ tptp.less tptp.x))) (let ((_let_2 (not (@ _let_1 tptp.z)))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (let ((_let_1 (@ tptp.less Xx))) (=> (@ _let_1 Xy) (=> (@ (@ tptp.less Xy) Xz) (@ _let_1 Xz))))))) (let ((_let_4 (= tptp.y tptp.z))) (let ((_let_5 (=> (not (@ (@ tptp.less tptp.y) tptp.z)) _let_4))) (let ((_let_6 (@ _let_1 tptp.y))) (let ((_let_7 (ho_3 k_2 tptp.x))) (let ((_let_8 (ho_4 _let_7 tptp.y))) (let ((_let_9 (ho_4 _let_7 tptp.z))) (let ((_let_10 (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_11 (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_12 (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_13 (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_14 (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_8)))))) (let ((_let_15 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_14 (PREPROCESS :args ((and _let_13 _let_12 _let_11 _let_10)))) :args ((and _let_8 _let_13 _let_12 _let_11 _let_10))) :args (0)))) (let ((_let_16 (not _let_9))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_16)))))) (let ((_let_18 (ho_4 (ho_3 k_2 tptp.y) tptp.z))) (let ((_let_19 (not _let_18))) (let ((_let_20 (not _let_8))) (let ((_let_21 (or _let_20 _let_19 _let_9))) (let ((_let_22 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (let ((_let_1 (ho_3 k_2 Xx))) (or (not (ho_4 _let_1 Xy)) (not (ho_4 (ho_3 k_2 Xy) Xz)) (ho_4 _let_1 Xz)))))) (let ((_let_23 (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) (Xz tptp.nat)) (let ((_let_1 (@ tptp.less Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ tptp.less Xy) Xz)) (@ _let_1 Xz)))) _let_22))))))) (let ((_let_24 (or))) (let ((_let_25 (_let_4))) (let ((_let_26 (not _let_4))) (let ((_let_27 (ASSUME :args _let_25))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_14 _let_27 _let_17) :args (_let_4 _let_8 _let_16)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_17)) (CONG (REFL :args (_let_7)) (SYMM _let_27) :args (APPLY_UF ho_4)) (TRUE_INTRO _let_14))) :args (_let_8 _let_4 _let_16)) :args ((not (and _let_4 _let_8 _let_16)) SB_LITERAL))) (CONG (REFL :args (_let_26)) (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_9))) :args _let_24)) :args ((or _let_9 _let_20 _let_26))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 (=> _let_19 _let_4)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) (REFL :args _let_25) :args _let_24)) :args ((or _let_4 _let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_19 _let_9 _let_20 (not _let_21)))) _let_17 _let_15 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.x tptp.y tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_22))) _let_23 :args (_let_21 false _let_22)) :args (_let_19 true _let_9 false _let_8 false _let_21)) :args (_let_4 true _let_18)) _let_17 _let_15 :args (false false _let_4 true _let_9 false _let_8)) :args (_let_6 _let_5 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_3 _let_2 true))))))))))))))))))))))))))))))
% 0.21/0.54 )
% 0.21/0.54 % SZS output end Proof for NUM664^1
% 0.21/0.54 % cvc5---1.0.5 exiting
% 0.21/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------