TSTP Solution File: NUM793^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM793^1 : 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 10:48:10 EDT 2023
% Result : Theorem 0.22s 0.55s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : NUM793^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n012.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri Aug 25 15:30:11 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 0.22/0.55 %------------------------------------------------------------------------------
% 0.22/0.55 % File : NUM793^1 : TPTP v8.1.2. Released v3.7.0.
% 0.22/0.55 % Domain : Number Theory
% 0.22/0.55 % Problem : Landau theorem 87d
% 0.22/0.55 % Version : Especial.
% 0.22/0.55 % English : more x0 z0
% 0.22/0.55
% 0.22/0.55 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.22/0.55 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.22/0.55 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.55 % Source : [Bro09]
% 0.22/0.55 % Names : satz87d [Lan30]
% 0.22/0.55 % : satz51d [Lan30]
% 0.22/0.55
% 0.22/0.55 % Status : Theorem
% 0.22/0.55 % : Without extensionality : Theorem
% 0.22/0.55 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.22/0.55 % Syntax : Number of formulae : 15 ( 3 unt; 8 typ; 0 def)
% 0.22/0.55 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.22/0.55 % Maximal formula atoms : 3 ( 1 avg)
% 0.22/0.55 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 24 @)
% 0.22/0.55 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.22/0.55 % Maximal formula depth : 8 ( 5 avg)
% 0.22/0.55 % Number of types : 2 ( 1 usr)
% 0.22/0.55 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.22/0.55 % Number of symbols : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.22/0.55 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.22/0.55 % SPC : TH0_THM_NEQ_NAR
% 0.22/0.55
% 0.22/0.55 % Comments :
% 0.22/0.55 %------------------------------------------------------------------------------
% 0.22/0.55 thf(rat_type,type,
% 0.22/0.55 rat: $tType ).
% 0.22/0.55
% 0.22/0.55 thf(x0,type,
% 0.22/0.55 x0: rat ).
% 0.22/0.55
% 0.22/0.55 thf(y0,type,
% 0.22/0.55 y0: rat ).
% 0.22/0.55
% 0.22/0.55 thf(z0,type,
% 0.22/0.55 z0: rat ).
% 0.22/0.55
% 0.22/0.55 thf(more,type,
% 0.22/0.55 more: rat > rat > $o ).
% 0.22/0.55
% 0.22/0.55 thf(m,axiom,
% 0.22/0.55 more @ x0 @ y0 ).
% 0.22/0.55
% 0.22/0.55 thf(moreis,type,
% 0.22/0.55 moreis: rat > rat > $o ).
% 0.22/0.55
% 0.22/0.55 thf(n,axiom,
% 0.22/0.55 moreis @ y0 @ z0 ).
% 0.22/0.55
% 0.22/0.55 thf(less,type,
% 0.22/0.55 less: rat > rat > $o ).
% 0.22/0.55
% 0.22/0.55 thf(satz83,axiom,
% 0.22/0.55 ! [Xx0: rat,Xy0: rat] :
% 0.22/0.55 ( ( less @ Xx0 @ Xy0 )
% 0.22/0.55 => ( more @ Xy0 @ Xx0 ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(lessis,type,
% 0.22/0.55 lessis: rat > rat > $o ).
% 0.22/0.55
% 0.22/0.55 thf(satz87a,axiom,
% 0.22/0.55 ! [Xx0: rat,Xy0: rat,Xz0: rat] :
% 0.22/0.55 ( ( lessis @ Xx0 @ Xy0 )
% 0.22/0.55 => ( ( less @ Xy0 @ Xz0 )
% 0.22/0.55 => ( less @ Xx0 @ Xz0 ) ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(satz84,axiom,
% 0.22/0.55 ! [Xx0: rat,Xy0: rat] :
% 0.22/0.55 ( ( moreis @ Xx0 @ Xy0 )
% 0.22/0.55 => ( lessis @ Xy0 @ Xx0 ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(satz82,axiom,
% 0.22/0.55 ! [Xx0: rat,Xy0: rat] :
% 0.22/0.55 ( ( more @ Xx0 @ Xy0 )
% 0.22/0.55 => ( less @ Xy0 @ Xx0 ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(satz87d,conjecture,
% 0.22/0.55 more @ x0 @ z0 ).
% 0.22/0.55
% 0.22/0.55 %------------------------------------------------------------------------------
% 0.22/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.48itvz04tA/cvc5---1.0.5_6113.p...
% 0.22/0.55 (declare-sort $$unsorted 0)
% 0.22/0.55 (declare-sort tptp.rat 0)
% 0.22/0.55 (declare-fun tptp.x0 () tptp.rat)
% 0.22/0.55 (declare-fun tptp.y0 () tptp.rat)
% 0.22/0.55 (declare-fun tptp.z0 () tptp.rat)
% 0.22/0.55 (declare-fun tptp.more (tptp.rat tptp.rat) Bool)
% 0.22/0.55 (assert (@ (@ tptp.more tptp.x0) tptp.y0))
% 0.22/0.55 (declare-fun tptp.moreis (tptp.rat tptp.rat) Bool)
% 0.22/0.55 (assert (@ (@ tptp.moreis tptp.y0) tptp.z0))
% 0.22/0.55 (declare-fun tptp.less (tptp.rat tptp.rat) Bool)
% 0.22/0.55 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.less Xx0) Xy0) (@ (@ tptp.more Xy0) Xx0))))
% 0.22/0.55 (declare-fun tptp.lessis (tptp.rat tptp.rat) Bool)
% 0.22/0.55 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat) (Xz0 tptp.rat)) (=> (@ (@ tptp.lessis Xx0) Xy0) (=> (@ (@ tptp.less Xy0) Xz0) (@ (@ tptp.less Xx0) Xz0)))))
% 0.22/0.55 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.moreis Xx0) Xy0) (@ (@ tptp.lessis Xy0) Xx0))))
% 0.22/0.55 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.more Xx0) Xy0) (@ (@ tptp.less Xy0) Xx0))))
% 0.22/0.55 (assert (not (@ (@ tptp.more tptp.x0) tptp.z0)))
% 0.22/0.55 (set-info :filename cvc5---1.0.5_6113)
% 0.22/0.55 (check-sat-assuming ( true ))
% 0.22/0.55 ------- get file name : TPTP file name is NUM793^1
% 0.22/0.55 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_6113.smt2...
% 0.22/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.55 % SZS status Theorem for NUM793^1
% 0.22/0.55 % SZS output start Proof for NUM793^1
% 0.22/0.55 (
% 0.22/0.55 (let ((_let_1 (@ tptp.more tptp.x0))) (let ((_let_2 (not (@ _let_1 tptp.z0)))) (let ((_let_3 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.more Xx0) Xy0) (@ (@ tptp.less Xy0) Xx0))))) (let ((_let_4 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.moreis Xx0) Xy0) (@ (@ tptp.lessis Xy0) Xx0))))) (let ((_let_5 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat) (Xz0 tptp.rat)) (=> (@ (@ tptp.lessis Xx0) Xy0) (=> (@ (@ tptp.less Xy0) Xz0) (@ (@ tptp.less Xx0) Xz0)))))) (let ((_let_6 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.less Xx0) Xy0) (@ (@ tptp.more Xy0) Xx0))))) (let ((_let_7 (@ (@ tptp.moreis tptp.y0) tptp.z0))) (let ((_let_8 (@ _let_1 tptp.y0))) (let ((_let_9 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat) (Xz0 tptp.rat)) (or (not (ho_4 (ho_3 k_7 Xx0) Xy0)) (not (ho_4 (ho_3 k_6 Xy0) Xz0)) (ho_4 (ho_3 k_6 Xx0) Xz0))))) (let ((_let_10 (ho_4 (ho_3 k_6 tptp.z0) tptp.x0))) (let ((_let_11 (ho_4 (ho_3 k_6 tptp.y0) tptp.x0))) (let ((_let_12 (not _let_11))) (let ((_let_13 (ho_4 (ho_3 k_7 tptp.z0) tptp.y0))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_10))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx0 tptp.rat) (Xy0 tptp.rat) (Xz0 tptp.rat)) (or (not (@ (@ tptp.lessis Xx0) Xy0)) (not (@ (@ tptp.less Xy0) Xz0)) (@ (@ tptp.less Xx0) Xz0))) _let_9))))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (ho_3 k_2 tptp.x0))) (let ((_let_19 (ho_4 _let_18 tptp.y0))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_11))) (let ((_let_22 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (ho_4 (ho_3 k_2 Xx0) Xy0)) (ho_4 (ho_3 k_6 Xy0) Xx0))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (@ (@ tptp.more Xx0) Xy0)) (@ (@ tptp.less Xy0) Xx0))) _let_22))))))) (let ((_let_24 (forall ((u |u_(-> tptp.rat Bool)|) (e Bool) (i tptp.rat)) (not (forall ((v |u_(-> tptp.rat Bool)|)) (not (forall ((ii tptp.rat)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_25 (forall ((x |u_(-> tptp.rat Bool)|) (y |u_(-> tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_26 (forall ((u |u_(-> tptp.rat tptp.rat Bool)|) (e |u_(-> tptp.rat Bool)|) (i tptp.rat)) (not (forall ((v |u_(-> tptp.rat tptp.rat Bool)|)) (not (forall ((ii tptp.rat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_27 (forall ((x |u_(-> tptp.rat tptp.rat Bool)|) (y |u_(-> tptp.rat tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_28 (ho_4 (ho_3 k_5 tptp.y0) tptp.z0))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_13))) (let ((_let_31 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (ho_4 (ho_3 k_5 Xx0) Xy0)) (ho_4 (ho_3 k_7 Xy0) Xx0))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (@ (@ tptp.moreis Xx0) Xy0)) (@ (@ tptp.lessis Xy0) Xx0))) _let_31))))))) (let ((_let_33 (ho_4 _let_18 tptp.z0))) (let ((_let_34 (not _let_10))) (let ((_let_35 (or _let_34 _let_33))) (let ((_let_36 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (ho_4 (ho_3 k_6 Xx0) Xy0)) (ho_4 (ho_3 k_2 Xy0) Xx0))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (@ (@ tptp.less Xx0) Xy0)) (@ (@ tptp.more Xy0) Xx0))) _let_36))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (tptp.z0 tptp.y0 tptp.x0 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_9))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_10 _let_14 _let_12 _let_17))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_33 _let_34 (not _let_35)))) (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 (not _let_33))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.z0 tptp.x0 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xy0) Xx0) true))))) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_34 true _let_33 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_13 (not _let_30)))) (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_28)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.y0 tptp.z0 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_5 Xx0) Xy0) false))))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_13 false _let_28 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_11 (not _let_21)))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_8)) (PREPROCESS :args ((= _let_8 _let_19)))) (PREPROCESS :args ((and _let_27 _let_26 _let_25 _let_24)))) :args ((and _let_19 _let_27 _let_26 _let_25 _let_24))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.x0 tptp.y0 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xx0) Xy0) false))))) :args (_let_22))) _let_23 :args (_let_21 false _let_22)) :args (_let_11 false _let_19 false _let_21)) :args (_let_17 true _let_10 false _let_13 false _let_11)) _let_16 :args (false true _let_15 false _let_9)) :args (_let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))
% 0.22/0.56 )
% 0.22/0.56 % SZS output end Proof for NUM793^1
% 0.22/0.56 % cvc5---1.0.5 exiting
% 0.22/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------