TSTP Solution File: NUM663^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM663^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 10:46:23 EDT 2023
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM663^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 09:51:32 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : NUM663^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.52 % Domain : Number Theory
% 0.21/0.52 % Problem : Landau theorem 16a
% 0.21/0.52 % Version : Especial.
% 0.21/0.52 % English : less x z
% 0.21/0.52
% 0.21/0.52 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.52 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.52 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.52 % Source : [Bro09]
% 0.21/0.52 % Names : satz16a [Lan30]
% 0.21/0.52
% 0.21/0.52 % Status : Theorem
% 0.21/0.52 % : Without extensionality : Theorem
% 0.21/0.52 % Rating : 0.15 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 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 v4.0.0, 0.33 v3.7.0
% 0.21/0.52 % Syntax : Number of formulae : 10 ( 2 unt; 5 typ; 0 def)
% 0.21/0.52 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.52 % Number of connectives : 19 ( 3 ~; 0 |; 0 &; 12 @)
% 0.21/0.52 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 8 ( 5 avg)
% 0.21/0.52 % Number of types : 2 ( 1 usr)
% 0.21/0.52 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.21/0.52 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.21/0.52 % SPC : TH0_THM_EQU_NAR
% 0.21/0.52
% 0.21/0.52 % Comments :
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(nat_type,type,
% 0.21/0.52 nat: $tType ).
% 0.21/0.52
% 0.21/0.52 thf(x,type,
% 0.21/0.52 x: nat ).
% 0.21/0.52
% 0.21/0.52 thf(y,type,
% 0.21/0.52 y: nat ).
% 0.21/0.52
% 0.21/0.52 thf(z,type,
% 0.21/0.52 z: nat ).
% 0.21/0.52
% 0.21/0.52 thf(less,type,
% 0.21/0.52 less: nat > nat > $o ).
% 0.21/0.52
% 0.21/0.52 thf(l,axiom,
% 0.21/0.52 ( ~ ( less @ x @ y )
% 0.21/0.52 => ( x = y ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(k,axiom,
% 0.21/0.52 less @ y @ z ).
% 0.21/0.52
% 0.21/0.52 thf(et,axiom,
% 0.21/0.52 ! [Xa: $o] :
% 0.21/0.52 ( ~ ~ Xa
% 0.21/0.52 => Xa ) ).
% 0.21/0.52
% 0.21/0.52 thf(satz15,axiom,
% 0.21/0.52 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.21/0.52 ( ( less @ Xx @ Xy )
% 0.21/0.52 => ( ( less @ Xy @ Xz )
% 0.21/0.52 => ( less @ Xx @ Xz ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(satz16a,conjecture,
% 0.21/0.52 less @ x @ z ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.vlb6FH997v/cvc5---1.0.5_7554.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-sort tptp.nat 0)
% 0.21/0.52 (declare-fun tptp.x () tptp.nat)
% 0.21/0.52 (declare-fun tptp.y () tptp.nat)
% 0.21/0.52 (declare-fun tptp.z () tptp.nat)
% 0.21/0.52 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.21/0.52 (assert (=> (not (@ (@ tptp.less tptp.x) tptp.y)) (= tptp.x tptp.y)))
% 0.21/0.52 (assert (@ (@ tptp.less tptp.y) tptp.z))
% 0.21/0.52 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.21/0.52 (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))))))
% 0.21/0.52 (assert (not (@ (@ tptp.less tptp.x) tptp.z)))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_7554)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is NUM663^1
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7554.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for NUM663^1
% 0.21/0.52 % SZS output start Proof for NUM663^1
% 0.21/0.52 (
% 0.21/0.52 (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.less tptp.y) tptp.z))) (let ((_let_5 (= tptp.x tptp.y))) (let ((_let_6 (=> (not (@ _let_1 tptp.y)) _let_5))) (let ((_let_7 (ho_4 (ho_3 k_2 tptp.y) tptp.z))) (let ((_let_8 (ho_3 k_2 tptp.x))) (let ((_let_9 (ho_4 _let_8 tptp.z))) (let ((_let_10 (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_7)))))) (let ((_let_11 (not _let_9))) (let ((_let_12 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_11)))))) (let ((_let_13 (ho_4 _let_8 tptp.y))) (let ((_let_14 (not _let_7))) (let ((_let_15 (not _let_13))) (let ((_let_16 (or _let_15 _let_14 _let_9))) (let ((_let_17 (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_18 (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_17))))))) (let ((_let_19 (or))) (let ((_let_20 (_let_5))) (let ((_let_21 (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_22 (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_23 (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_24 (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_25 (=> _let_15 _let_5))) (let ((_let_26 (not _let_5))) (let ((_let_27 (ASSUME :args _let_20))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_12 _let_27 _let_10) :args (_let_5 _let_7 _let_11)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_10)) (CONG (CONG (REFL :args (k_2)) (SYMM _let_27) :args (APPLY_UF ho_3)) (REFL :args (tptp.z)) :args (APPLY_UF ho_4)) (FALSE_INTRO _let_12))) :args (_let_11 _let_5 _let_7)) :args ((not (and _let_5 _let_7 _let_11)) SB_LITERAL))) (CONG (REFL :args (_let_26)) (REFL :args (_let_14)) (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_9))) :args _let_19)) :args ((or _let_9 _let_26 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_25)))) (PREPROCESS :args ((and _let_24 _let_23 _let_22 _let_21)))) :args ((and _let_25 _let_24 _let_23 _let_22 _let_21))) :args (0))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_13))) (REFL :args _let_20) :args _let_19)) :args ((or _let_5 _let_13))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_9 _let_14 (not _let_16)))) _let_12 _let_10 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (tptp.x tptp.y tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_17))) _let_18 :args (_let_16 false _let_17)) :args (_let_15 true _let_9 false _let_7 false _let_16)) :args (_let_5 true _let_13)) _let_12 _let_10 :args (false false _let_5 true _let_9 false _let_7)) :args (_let_6 _let_4 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_3 _let_2 true))))))))))))))))))))))))))))))
% 0.21/0.52 )
% 0.21/0.52 % SZS output end Proof for NUM663^1
% 0.21/0.52 % cvc5---1.0.5 exiting
% 0.21/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------