TSTP Solution File: NUM682^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 10:46:40 EDT 2023
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n029.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 : Fri Aug 25 16:55:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 % File : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.51 % Domain : Number Theory
% 0.21/0.51 % Problem : Landau theorem 20c
% 0.21/0.51 % Version : Especial.
% 0.21/0.51 % English : less x y
% 0.21/0.51
% 0.21/0.51 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.51 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.51 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.51 % Source : [Bro09]
% 0.21/0.51 % Names : satz20c [Lan30]
% 0.21/0.51 % : satz33c [Lan30]
% 0.21/0.51
% 0.21/0.51 % Status : Theorem
% 0.21/0.51 % : Without extensionality : Theorem
% 0.21/0.51 % Rating : 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.29 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 v4.0.1, 0.33 v3.7.0
% 0.21/0.51 % Syntax : Number of formulae : 14 ( 2 unt; 7 typ; 0 def)
% 0.21/0.51 % Number of atoms : 15 ( 5 equ; 0 cnn)
% 0.21/0.51 % Maximal formula atoms : 6 ( 2 avg)
% 0.21/0.51 % Number of connectives : 53 ( 11 ~; 0 |; 0 &; 32 @)
% 0.21/0.51 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.21/0.51 % Maximal formula depth : 12 ( 7 avg)
% 0.21/0.51 % Number of types : 2 ( 1 usr)
% 0.21/0.51 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.21/0.51 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.21/0.51 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.21/0.51 % SPC : TH0_THM_EQU_NAR
% 0.21/0.51
% 0.21/0.51 % Comments :
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 thf(nat_type,type,
% 0.21/0.51 nat: $tType ).
% 0.21/0.51
% 0.21/0.51 thf(x,type,
% 0.21/0.51 x: nat ).
% 0.21/0.51
% 0.21/0.51 thf(y,type,
% 0.21/0.51 y: nat ).
% 0.21/0.51
% 0.21/0.51 thf(z,type,
% 0.21/0.51 z: nat ).
% 0.21/0.51
% 0.21/0.51 thf(less,type,
% 0.21/0.51 less: nat > nat > $o ).
% 0.21/0.51
% 0.21/0.51 thf(pl,type,
% 0.21/0.51 pl: nat > nat > nat ).
% 0.21/0.51
% 0.21/0.51 thf(l,axiom,
% 0.21/0.51 less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ).
% 0.21/0.51
% 0.21/0.51 thf(et,axiom,
% 0.21/0.51 ! [Xa: $o] :
% 0.21/0.51 ( ~ ~ Xa
% 0.21/0.51 => Xa ) ).
% 0.21/0.51
% 0.21/0.51 thf(more,type,
% 0.21/0.51 more: nat > nat > $o ).
% 0.21/0.51
% 0.21/0.51 thf(satz10b,axiom,
% 0.21/0.51 ! [Xx: nat,Xy: nat] :
% 0.21/0.51 ~ ( ( ( Xx = Xy )
% 0.21/0.51 => ~ ( more @ Xx @ Xy ) )
% 0.21/0.51 => ~ ~ ( ( ( more @ Xx @ Xy )
% 0.21/0.51 => ~ ( less @ Xx @ Xy ) )
% 0.21/0.51 => ~ ( ( less @ Xx @ Xy )
% 0.21/0.51 => ( Xx != Xy ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz19a,axiom,
% 0.21/0.51 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.21/0.51 ( ( more @ Xx @ Xy )
% 0.21/0.51 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz19b,axiom,
% 0.21/0.51 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.21/0.51 ( ( Xx = Xy )
% 0.21/0.51 => ( ( pl @ Xx @ Xz )
% 0.21/0.51 = ( pl @ Xy @ Xz ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz10a,axiom,
% 0.21/0.51 ! [Xx: nat,Xy: nat] :
% 0.21/0.51 ( ( Xx != Xy )
% 0.21/0.51 => ( ~ ( more @ Xx @ Xy )
% 0.21/0.51 => ( less @ Xx @ Xy ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz20c,conjecture,
% 0.21/0.51 less @ x @ y ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8a7l7jFcBB/cvc5---1.0.5_8593.p...
% 0.21/0.51 (declare-sort $$unsorted 0)
% 0.21/0.51 (declare-sort tptp.nat 0)
% 0.21/0.51 (declare-fun tptp.x () tptp.nat)
% 0.21/0.51 (declare-fun tptp.y () tptp.nat)
% 0.21/0.51 (declare-fun tptp.z () tptp.nat)
% 0.21/0.51 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.21/0.51 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.21/0.51 (assert (@ (@ tptp.less (@ (@ tptp.pl tptp.x) tptp.z)) (@ (@ tptp.pl tptp.y) tptp.z)))
% 0.21/0.51 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.21/0.51 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.21/0.51 (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)))))))))))))
% 0.21/0.51 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xz)))))
% 0.21/0.51 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (= Xx Xy) (= (@ (@ tptp.pl Xx) Xz) (@ (@ tptp.pl Xy) Xz)))))
% 0.21/0.51 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (not (= Xx Xy)) (=> (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.less Xx) Xy)))))
% 0.21/0.51 (assert (not (@ (@ tptp.less tptp.x) tptp.y)))
% 0.21/0.51 (set-info :filename cvc5---1.0.5_8593)
% 0.21/0.51 (check-sat-assuming ( true ))
% 0.21/0.51 ------- get file name : TPTP file name is NUM682^1
% 0.21/0.54 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8593.smt2...
% 0.21/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.54 % SZS status Theorem for NUM682^1
% 0.21/0.54 % SZS output start Proof for NUM682^1
% 0.21/0.54 (
% 0.21/0.54 (let ((_let_1 (not (@ (@ tptp.less tptp.x) tptp.y)))) (let ((_let_2 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (not (= Xx Xy)) (=> (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.less Xx) Xy)))))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xz)))))) (let ((_let_4 (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_5 (@ (@ tptp.less (@ (@ tptp.pl tptp.x) tptp.z)) (@ (@ tptp.pl tptp.y) tptp.z)))) (let ((_let_6 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (or (not (ho_7 (ho_6 k_8 Xx) Xy)) (ho_7 (ho_6 k_8 (ho_4 (ho_3 k_2 Xx) Xz)) (ho_4 (ho_3 k_2 Xy) Xz)))))) (let ((_let_7 (ho_4 (ho_3 k_2 tptp.y) tptp.z))) (let ((_let_8 (ho_4 (ho_3 k_2 tptp.x) tptp.z))) (let ((_let_9 (ho_7 (ho_6 k_8 _let_8) _let_7))) (let ((_let_10 (ho_7 (ho_6 k_8 tptp.x) tptp.y))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (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)) (or (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xz)))) _let_6))))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (ho_7 (ho_6 k_5 tptp.x) tptp.y))) (let ((_let_16 (= tptp.x tptp.y))) (let ((_let_17 (or _let_16 _let_10 _let_15))) (let ((_let_18 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (= Xx Xy) (ho_7 (ho_6 k_8 Xx) Xy) (ho_7 (ho_6 k_5 Xx) Xy))))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 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_18))))))) (let ((_let_20 (ho_6 k_5 _let_8))) (let ((_let_21 (ho_7 _let_20 _let_8))) (let ((_let_22 (ho_7 _let_20 _let_7))) (let ((_let_23 (not _let_16))) (let ((_let_24 (forall ((BOUND_VARIABLE_699 tptp.nat)) (not (ho_7 (ho_6 k_5 BOUND_VARIABLE_699) BOUND_VARIABLE_699))))) (let ((_let_25 (not _let_21))) (let ((_let_26 (forall ((BOUND_VARIABLE_684 tptp.nat) (BOUND_VARIABLE_686 tptp.nat)) (or (not (ho_7 (ho_6 k_8 BOUND_VARIABLE_684) BOUND_VARIABLE_686)) (not (ho_7 (ho_6 k_5 BOUND_VARIABLE_684) BOUND_VARIABLE_686)))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_674 tptp.nat)) (not (@ (@ tptp.more BOUND_VARIABLE_674) BOUND_VARIABLE_674))) (forall ((BOUND_VARIABLE_684 tptp.nat) (BOUND_VARIABLE_686 tptp.nat)) (or (not (@ (@ tptp.more BOUND_VARIABLE_684) BOUND_VARIABLE_686)) (not (@ (@ tptp.less BOUND_VARIABLE_684) BOUND_VARIABLE_686)))) (forall ((BOUND_VARIABLE_699 tptp.nat)) (not (@ (@ tptp.less BOUND_VARIABLE_699) BOUND_VARIABLE_699)))) (and (forall ((BOUND_VARIABLE_674 tptp.nat)) (not (ho_7 (ho_6 k_8 BOUND_VARIABLE_674) BOUND_VARIABLE_674))) _let_26 _let_24)))))))) (let ((_let_28 (_let_24))) (let ((_let_29 (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_30 (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_31 (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_32 (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_33 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_35 (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_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_22)))))) (let ((_let_38 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_37 (PREPROCESS :args ((and _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29)))) :args ((and _let_22 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29))) :args (0)))) (let ((_let_39 (not _let_22))) (let ((_let_40 (ASSUME :args (_let_16)))) (let ((_let_41 (ASSUME :args (_let_25)))) (let ((_let_42 (not _let_9))) (let ((_let_43 (or _let_42 _let_39))) (let ((_let_44 (_let_26))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (tptp.x tptp.y tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_6))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_9 _let_11 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_39 _let_42 (not _let_43)))) _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (_let_8 _let_7 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_7 (ho_6 k_5 BOUND_VARIABLE_684) BOUND_VARIABLE_686) false))))) :args _let_44)) (AND_ELIM _let_27 :args (1)) :args (_let_43 false _let_26)) :args (_let_42 false _let_22 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_15 _let_16 _let_10 (not _let_17)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_15))))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_37 _let_40 _let_41) :args (_let_22 _let_25 _let_16)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_41)) (CONG (REFL :args (_let_20)) (CONG (CONG (REFL :args (k_2)) (SYMM (SYMM _let_40)) :args (APPLY_UF ho_3)) (REFL :args (tptp.z)) :args (APPLY_UF ho_4)) :args (APPLY_UF ho_7)) (TRUE_INTRO _let_37))) :args (_let_22 _let_16 _let_25)) :args ((not (and _let_22 _let_25 _let_16)) SB_LITERAL))) (CONG (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_21))) (REFL :args (_let_23)) :args (or))) _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_28) :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 BOUND_VARIABLE_699)))) :args _let_28)) (AND_ELIM _let_27 :args (2)) :args (_let_25 false _let_24)) :args (_let_23 false _let_22 true _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING ((not (= (ho_7 (ho_6 k_5 Xx) Xy) true))))) :args (_let_18))) _let_19 :args (_let_17 false _let_18)) :args (_let_10 true _let_15 true _let_16 false _let_17)) :args (_let_14 true _let_9 false _let_10)) _let_13 :args (false true _let_12 false _let_6)) :args (_let_5 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_4 _let_3 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (= Xx Xy) (= (@ (@ tptp.pl Xx) Xz) (@ (@ tptp.pl Xy) Xz)))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.54 )
% 0.21/0.54 % SZS output end Proof for NUM682^1
% 0.21/0.54 % cvc5---1.0.5 exiting
% 0.21/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------