TSTP Solution File: NUM795^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM795^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM795^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n020.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 13:35:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 % File : NUM795^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.50 % Domain : Number Theory
% 0.20/0.50 % Problem : Landau theorem 99c
% 0.20/0.50 % Version : Especial.
% 0.20/0.50 % English : less (pl x0 z0) (pl y0 u0)
% 0.20/0.50
% 0.20/0.50 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.50 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.50 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.50 % Source : [Bro09]
% 0.20/0.50 % Names : satz99c [Lan30]
% 0.20/0.50 % : satz75c [Lan30]
% 0.20/0.50 % : satz65c [Lan30]
% 0.20/0.50
% 0.20/0.50 % Status : Theorem
% 0.20/0.50 % : Without extensionality : Theorem
% 0.20/0.50 % Rating : 0.00 v3.7.0
% 0.20/0.50 % Syntax : Number of formulae : 17 ( 3 unt; 10 typ; 0 def)
% 0.20/0.50 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.20/0.50 % Maximal formula atoms : 3 ( 1 avg)
% 0.20/0.50 % Number of connectives : 37 ( 0 ~; 0 |; 0 &; 32 @)
% 0.20/0.50 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.50 % Maximal formula depth : 11 ( 6 avg)
% 0.20/0.50 % Number of types : 2 ( 1 usr)
% 0.20/0.50 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.20/0.50 % Number of symbols : 9 ( 9 usr; 4 con; 0-2 aty)
% 0.20/0.50 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.20/0.50 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.50
% 0.20/0.50 % Comments :
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 thf(rat_type,type,
% 0.20/0.50 rat: $tType ).
% 0.20/0.50
% 0.20/0.50 thf(x0,type,
% 0.20/0.50 x0: rat ).
% 0.20/0.50
% 0.20/0.50 thf(y0,type,
% 0.20/0.50 y0: rat ).
% 0.20/0.50
% 0.20/0.50 thf(z0,type,
% 0.20/0.50 z0: rat ).
% 0.20/0.50
% 0.20/0.50 thf(u0,type,
% 0.20/0.50 u0: rat ).
% 0.20/0.50
% 0.20/0.50 thf(lessis,type,
% 0.20/0.50 lessis: rat > rat > $o ).
% 0.20/0.50
% 0.20/0.50 thf(l,axiom,
% 0.20/0.50 lessis @ x0 @ y0 ).
% 0.20/0.50
% 0.20/0.50 thf(less,type,
% 0.20/0.50 less: rat > rat > $o ).
% 0.20/0.50
% 0.20/0.50 thf(k,axiom,
% 0.20/0.50 less @ z0 @ u0 ).
% 0.20/0.50
% 0.20/0.50 thf(pl,type,
% 0.20/0.50 pl: rat > rat > rat ).
% 0.20/0.50
% 0.20/0.50 thf(more,type,
% 0.20/0.50 more: rat > rat > $o ).
% 0.20/0.50
% 0.20/0.50 thf(satz82,axiom,
% 0.20/0.50 ! [Xx0: rat,Xy0: rat] :
% 0.20/0.50 ( ( more @ Xx0 @ Xy0 )
% 0.20/0.50 => ( less @ Xy0 @ Xx0 ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(moreis,type,
% 0.20/0.50 moreis: rat > rat > $o ).
% 0.20/0.50
% 0.20/0.50 thf(satz99a,axiom,
% 0.20/0.50 ! [Xx0: rat,Xy0: rat,Xz0: rat,Xu0: rat] :
% 0.20/0.50 ( ( moreis @ Xx0 @ Xy0 )
% 0.20/0.50 => ( ( more @ Xz0 @ Xu0 )
% 0.20/0.50 => ( more @ ( pl @ Xx0 @ Xz0 ) @ ( pl @ Xy0 @ Xu0 ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(satz85,axiom,
% 0.20/0.50 ! [Xx0: rat,Xy0: rat] :
% 0.20/0.50 ( ( lessis @ Xx0 @ Xy0 )
% 0.20/0.50 => ( moreis @ Xy0 @ Xx0 ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(satz83,axiom,
% 0.20/0.50 ! [Xx0: rat,Xy0: rat] :
% 0.20/0.50 ( ( less @ Xx0 @ Xy0 )
% 0.20/0.50 => ( more @ Xy0 @ Xx0 ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(satz99c,conjecture,
% 0.20/0.50 less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.nwBDIpEyA9/cvc5---1.0.5_19247.p...
% 0.20/0.50 (declare-sort $$unsorted 0)
% 0.20/0.50 (declare-sort tptp.rat 0)
% 0.20/0.50 (declare-fun tptp.x0 () tptp.rat)
% 0.20/0.50 (declare-fun tptp.y0 () tptp.rat)
% 0.20/0.50 (declare-fun tptp.z0 () tptp.rat)
% 0.20/0.50 (declare-fun tptp.u0 () tptp.rat)
% 0.20/0.50 (declare-fun tptp.lessis (tptp.rat tptp.rat) Bool)
% 0.20/0.50 (assert (@ (@ tptp.lessis tptp.x0) tptp.y0))
% 0.20/0.50 (declare-fun tptp.less (tptp.rat tptp.rat) Bool)
% 0.20/0.50 (assert (@ (@ tptp.less tptp.z0) tptp.u0))
% 0.20/0.50 (declare-fun tptp.pl (tptp.rat tptp.rat) tptp.rat)
% 0.20/0.50 (declare-fun tptp.more (tptp.rat tptp.rat) Bool)
% 0.20/0.50 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.more Xx0) Xy0) (@ (@ tptp.less Xy0) Xx0))))
% 0.20/0.50 (declare-fun tptp.moreis (tptp.rat tptp.rat) Bool)
% 0.20/0.50 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat) (Xz0 tptp.rat) (Xu0 tptp.rat)) (=> (@ (@ tptp.moreis Xx0) Xy0) (=> (@ (@ tptp.more Xz0) Xu0) (@ (@ tptp.more (@ (@ tptp.pl Xx0) Xz0)) (@ (@ tptp.pl Xy0) Xu0))))))
% 0.20/0.50 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.lessis Xx0) Xy0) (@ (@ tptp.moreis Xy0) Xx0))))
% 0.20/0.50 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.less Xx0) Xy0) (@ (@ tptp.more Xy0) Xx0))))
% 0.20/0.50 (assert (not (@ (@ tptp.less (@ (@ tptp.pl tptp.x0) tptp.z0)) (@ (@ tptp.pl tptp.y0) tptp.u0))))
% 0.20/0.50 (set-info :filename cvc5---1.0.5_19247)
% 0.20/0.50 (check-sat-assuming ( true ))
% 0.20/0.50 ------- get file name : TPTP file name is NUM795^1
% 0.20/0.50 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19247.smt2...
% 0.20/0.50 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for NUM795^1
% 0.20/0.53 % SZS output start Proof for NUM795^1
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (not (@ (@ tptp.less (@ (@ tptp.pl tptp.x0) tptp.z0)) (@ (@ tptp.pl tptp.y0) tptp.u0))))) (let ((_let_2 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.less Xx0) Xy0) (@ (@ tptp.more Xy0) Xx0))))) (let ((_let_3 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.lessis Xx0) Xy0) (@ (@ tptp.moreis Xy0) Xx0))))) (let ((_let_4 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat) (Xz0 tptp.rat) (Xu0 tptp.rat)) (=> (@ (@ tptp.moreis Xx0) Xy0) (=> (@ (@ tptp.more Xz0) Xu0) (@ (@ tptp.more (@ (@ tptp.pl Xx0) Xz0)) (@ (@ tptp.pl Xy0) Xu0))))))) (let ((_let_5 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (=> (@ (@ tptp.more Xx0) Xy0) (@ (@ tptp.less Xy0) Xx0))))) (let ((_let_6 (@ (@ tptp.less tptp.z0) tptp.u0))) (let ((_let_7 (@ (@ tptp.lessis tptp.x0) tptp.y0))) (let ((_let_8 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat) (Xz0 tptp.rat) (Xu0 tptp.rat)) (or (not (ho_4 (ho_3 k_10 Xx0) Xy0)) (not (ho_4 (ho_3 k_6 Xz0) Xu0)) (ho_4 (ho_3 k_6 (ho_9 (ho_8 k_7 Xx0) Xz0)) (ho_9 (ho_8 k_7 Xy0) Xu0)))))) (let ((_let_9 (ho_9 (ho_8 k_7 tptp.x0) tptp.z0))) (let ((_let_10 (ho_9 (ho_8 k_7 tptp.y0) tptp.u0))) (let ((_let_11 (ho_4 (ho_3 k_6 _let_10) _let_9))) (let ((_let_12 (ho_4 (ho_3 k_6 tptp.u0) tptp.z0))) (let ((_let_13 (not _let_12))) (let ((_let_14 (ho_4 (ho_3 k_10 tptp.y0) tptp.x0))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_11))) (let ((_let_17 (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) (Xz0 tptp.rat) (Xu0 tptp.rat)) (or (not (@ (@ tptp.moreis Xx0) Xy0)) (not (@ (@ tptp.more Xz0) Xu0)) (@ (@ tptp.more (@ (@ tptp.pl Xx0) Xz0)) (@ (@ tptp.pl Xy0) Xu0)))) _let_8))))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (ho_4 (ho_3 k_5 tptp.z0) tptp.u0))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_12))) (let ((_let_22 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (ho_4 (ho_3 k_5 Xx0) Xy0)) (ho_4 (ho_3 k_6 Xy0) Xx0))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (@ (@ tptp.less Xx0) Xy0)) (@ (@ tptp.more Xy0) Xx0))) _let_22))))))) (let ((_let_24 (ho_4 (ho_3 k_2 tptp.x0) tptp.y0))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_14))) (let ((_let_27 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (ho_4 (ho_3 k_2 Xx0) Xy0)) (ho_4 (ho_3 k_10 Xy0) Xx0))))) (let ((_let_28 (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.lessis Xx0) Xy0)) (@ (@ tptp.moreis Xy0) Xx0))) _let_27))))))) (let ((_let_29 (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_30 (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_31 (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_32 (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_33 (forall ((u |u_(-> tptp.rat tptp.rat)|) (e tptp.rat) (i tptp.rat)) (not (forall ((v |u_(-> tptp.rat tptp.rat)|)) (not (forall ((ii tptp.rat)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_35 (forall ((u |u_(-> tptp.rat tptp.rat tptp.rat)|) (e |u_(-> tptp.rat tptp.rat)|) (i tptp.rat)) (not (forall ((v |u_(-> tptp.rat tptp.rat tptp.rat)|)) (not (forall ((ii tptp.rat)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_37 (ho_4 (ho_3 k_5 _let_9) _let_10))) (let ((_let_38 (not _let_11))) (let ((_let_39 (or _let_38 _let_37))) (let ((_let_40 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (or (not (ho_4 (ho_3 k_6 Xx0) Xy0)) (ho_4 (ho_3 k_5 Xy0) Xx0))))) (let ((_let_41 (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)) (or (not (@ (@ tptp.more Xx0) Xy0)) (@ (@ tptp.less Xy0) Xx0))) _let_40))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (tptp.y0 tptp.x0 tptp.u0 tptp.z0 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_8))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_11 _let_15 _let_13 _let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_37 _let_38 (not _let_39)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_37))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_10 _let_9 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_5 Xy0) Xx0) true))))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_38 true _let_37 false _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_14 (not _let_26)))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_24)))) (PREPROCESS :args ((and _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29)))) :args ((and _let_24 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.x0 tptp.y0 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xx0) Xy0) false))))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_14 false _let_24 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_12 (not _let_21)))) (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_19)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.z0 tptp.u0 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_5 Xx0) Xy0) false))))) :args (_let_22))) _let_23 :args (_let_21 false _let_22)) :args (_let_12 false _let_19 false _let_21)) :args (_let_18 true _let_11 false _let_14 false _let_12)) _let_17 :args (false true _let_16 false _let_8)) :args (_let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.53 )
% 0.20/0.53 % SZS output end Proof for NUM795^1
% 0.20/0.53 % cvc5---1.0.5 exiting
% 0.20/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------