TSTP Solution File: NUM653^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM653^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 10:46:11 EDT 2023
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM653^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.10 % Command : do_cvc5 %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Fri Aug 25 10:17:58 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.39 %----Proving TH0
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 % File : NUM653^1 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.41 % Domain : Number Theory
% 0.14/0.41 % Problem : Landau theorem 10d
% 0.14/0.41 % Version : Especial.
% 0.14/0.41 % English : ~(more x y)
% 0.14/0.41
% 0.14/0.41 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.14/0.41 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.14/0.41 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.14/0.41 % Source : [Bro09]
% 0.14/0.41 % Names : satz10d [Lan30]
% 0.14/0.41
% 0.14/0.41 % Status : Theorem
% 0.14/0.41 % : Without extensionality : Theorem
% 0.14/0.41 % Rating : 0.15 v8.1.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.14/0.41 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.14/0.41 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.14/0.41 % Maximal formula atoms : 6 ( 2 avg)
% 0.14/0.41 % Number of connectives : 30 ( 11 ~; 0 |; 0 &; 12 @)
% 0.14/0.41 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.14/0.41 % Maximal formula depth : 12 ( 7 avg)
% 0.14/0.41 % Number of types : 2 ( 1 usr)
% 0.14/0.41 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.14/0.41 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.14/0.41 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.14/0.41 % SPC : TH0_THM_EQU_NAR
% 0.14/0.41
% 0.14/0.41 % Comments :
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 thf(nat_type,type,
% 0.14/0.41 nat: $tType ).
% 0.14/0.41
% 0.14/0.41 thf(x,type,
% 0.14/0.41 x: nat ).
% 0.14/0.41
% 0.14/0.41 thf(y,type,
% 0.14/0.41 y: nat ).
% 0.14/0.41
% 0.14/0.41 thf(less,type,
% 0.14/0.41 less: nat > nat > $o ).
% 0.14/0.41
% 0.14/0.41 thf(l,axiom,
% 0.14/0.41 ( ~ ( less @ x @ y )
% 0.14/0.41 => ( x = y ) ) ).
% 0.14/0.41
% 0.14/0.41 thf(more,type,
% 0.14/0.41 more: nat > nat > $o ).
% 0.14/0.41
% 0.14/0.41 thf(et,axiom,
% 0.14/0.41 ! [Xa: $o] :
% 0.14/0.41 ( ~ ~ Xa
% 0.14/0.41 => Xa ) ).
% 0.14/0.41
% 0.14/0.41 thf(satz10b,axiom,
% 0.14/0.41 ! [Xx: nat,Xy: nat] :
% 0.14/0.41 ~ ( ( ( Xx = Xy )
% 0.14/0.41 => ~ ( more @ Xx @ Xy ) )
% 0.14/0.41 => ~ ~ ( ( ( more @ Xx @ Xy )
% 0.14/0.41 => ~ ( less @ Xx @ Xy ) )
% 0.14/0.41 => ~ ( ( less @ Xx @ Xy )
% 0.14/0.41 => ( Xx != Xy ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 thf(satz10d,conjecture,
% 0.14/0.41 ~ ( more @ x @ y ) ).
% 0.14/0.41
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.IK8CQCHyuY/cvc5---1.0.5_17991.p...
% 0.14/0.41 (declare-sort $$unsorted 0)
% 0.14/0.41 (declare-sort tptp.nat 0)
% 0.14/0.41 (declare-fun tptp.x () tptp.nat)
% 0.14/0.41 (declare-fun tptp.y () tptp.nat)
% 0.14/0.41 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.14/0.41 (assert (=> (not (@ (@ tptp.less tptp.x) tptp.y)) (= tptp.x tptp.y)))
% 0.14/0.41 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.14/0.41 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.14/0.41 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (let ((_let_1 (= Xx Xy))) (let ((_let_2 (@ (@ tptp.less Xx) Xy))) (let ((_let_3 (@ (@ tptp.more Xx) Xy))) (not (=> (=> _let_1 (not _let_3)) (not (not (=> (=> _let_3 (not _let_2)) (not (=> _let_2 (not _let_1)))))))))))))
% 0.14/0.41 (assert (not (not (@ (@ tptp.more tptp.x) tptp.y))))
% 0.14/0.41 (set-info :filename cvc5---1.0.5_17991)
% 0.14/0.41 (check-sat-assuming ( true ))
% 0.14/0.41 ------- get file name : TPTP file name is NUM653^1
% 0.14/0.41 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17991.smt2...
% 0.14/0.41 --- Run --ho-elim --full-saturate-quant at 10...
% 0.14/0.41 % SZS status Theorem for NUM653^1
% 0.14/0.41 % SZS output start Proof for NUM653^1
% 0.14/0.41 (
% 0.14/0.41 (let ((_let_1 (@ (@ tptp.more tptp.x) tptp.y))) (let ((_let_2 (not (not _let_1)))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat)) (let ((_let_1 (= Xx Xy))) (let ((_let_2 (@ (@ tptp.less Xx) Xy))) (let ((_let_3 (@ (@ tptp.more Xx) Xy))) (not (=> (=> _let_1 (not _let_3)) (not (not (=> (=> _let_3 (not _let_2)) (not (=> _let_2 (not _let_1)))))))))))))) (let ((_let_4 (= tptp.x tptp.y))) (let ((_let_5 (=> (not (@ (@ tptp.less tptp.x) tptp.y)) _let_4))) (let ((_let_6 (forall ((BOUND_VARIABLE_631 tptp.nat)) (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_631) BOUND_VARIABLE_631))))) (let ((_let_7 (ho_4 (ho_3 k_5 tptp.y) tptp.y))) (let ((_let_8 (0))) (let ((_let_9 (forall ((BOUND_VARIABLE_641 tptp.nat) (BOUND_VARIABLE_643 tptp.nat)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_641) BOUND_VARIABLE_643)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_641) BOUND_VARIABLE_643)))))) (let ((_let_10 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_631 tptp.nat)) (not (@ (@ tptp.more BOUND_VARIABLE_631) BOUND_VARIABLE_631))) (forall ((BOUND_VARIABLE_641 tptp.nat) (BOUND_VARIABLE_643 tptp.nat)) (or (not (@ (@ tptp.more BOUND_VARIABLE_641) BOUND_VARIABLE_643)) (not (@ (@ tptp.less BOUND_VARIABLE_641) BOUND_VARIABLE_643)))) (forall ((BOUND_VARIABLE_656 tptp.nat)) (not (@ (@ tptp.less BOUND_VARIABLE_656) BOUND_VARIABLE_656)))) (and _let_6 _let_9 (forall ((BOUND_VARIABLE_656 tptp.nat)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_656) BOUND_VARIABLE_656))))))))))) (let ((_let_11 (ho_4 (ho_3 k_5 tptp.x) tptp.y))) (let ((_let_12 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_1 _let_11))))))) (let ((_let_13 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_14 (not _let_13))) (let ((_let_15 (not _let_11))) (let ((_let_16 (or _let_15 _let_14))) (let ((_let_17 (_let_9))) (let ((_let_18 (_let_4))) (let ((_let_19 (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_20 (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_21 (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_22 (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_23 (=> _let_14 _let_4))) (let ((_let_24 (and _let_4 _let_11))) (let ((_let_25 (ASSUME :args _let_18))) (let ((_let_26 (_let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args (tptp.y QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_26)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_24)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_12 _let_25) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (REFL :args (k_5)) (SYMM _let_25) :args (APPLY_UF ho_3)) (REFL :args (tptp.y)) :args (APPLY_UF ho_4)) (TRUE_INTRO _let_12))) :args (_let_11 _let_4))) :args (_let_4 _let_11))) :args (true _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_23)))) (PREPROCESS :args ((and _let_22 _let_21 _let_20 _let_19)))) :args ((and _let_23 _let_22 _let_21 _let_20 _let_19))) :args _let_8)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) (REFL :args _let_18) :args (or))) :args ((or _let_4 _let_13))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_14 _let_15 (not _let_16)))) _let_12 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_17) :args (tptp.x tptp.y QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_17)) (AND_ELIM _let_10 :args (1)) :args (_let_16 false _let_9)) :args (_let_14 false _let_11 false _let_16)) :args (_let_4 true _let_13)) _let_12 :args (_let_7 false _let_4 false _let_11)) (AND_ELIM _let_10 :args _let_8) :args (false false _let_7 false _let_6)) :args (_let_5 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_3 _let_2 true)))))))))))))))))))))))))))))
% 0.14/0.42 )
% 0.14/0.42 % SZS output end Proof for NUM653^1
% 0.14/0.42 % cvc5---1.0.5 exiting
% 0.14/0.42 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------