TSTP Solution File: NUM016^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 10:42:00 EDT 2023
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n018.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 08:54:14 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 % File : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.49 % Domain : Number Theory
% 0.21/0.49 % Problem : TPS problem NUM016-1
% 0.21/0.49 % Version : Especial.
% 0.21/0.49 % English : There exist infinitely many primes.
% 0.21/0.49
% 0.21/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.49 % Source : [Bro09]
% 0.21/0.49 % Names : tps_0442 [Bro09]
% 0.21/0.49 % : NUM016-1 [TPS]
% 0.21/0.49
% 0.21/0.49 % Status : Theorem
% 0.21/0.49 % Rating : 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.21/0.49 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.21/0.49 % Number of atoms : 22 ( 0 equ; 0 cnn)
% 0.21/0.49 % Maximal formula atoms : 22 ( 22 avg)
% 0.21/0.49 % Number of connectives : 76 ( 11 ~; 10 |; 11 &; 44 @)
% 0.21/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.21/0.49 % Maximal formula depth : 19 ( 19 avg)
% 0.21/0.49 % Number of types : 2 ( 0 usr)
% 0.21/0.49 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.21/0.49 % Number of symbols : 6 ( 6 usr; 1 con; 0-2 aty)
% 0.21/0.49 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.21/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.49
% 0.21/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.49 % :
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 thf(a,type,
% 0.21/0.49 a: $i ).
% 0.21/0.49
% 0.21/0.49 thf(factorial_plus_one,type,
% 0.21/0.49 factorial_plus_one: $i > $i ).
% 0.21/0.49
% 0.21/0.49 thf(less,type,
% 0.21/0.49 less: $i > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(prime,type,
% 0.21/0.49 prime: $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(prime_divisor,type,
% 0.21/0.49 prime_divisor: $i > $i ).
% 0.21/0.49
% 0.21/0.49 thf(divides,type,
% 0.21/0.49 divides: $i > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(cNUM016_1,conjecture,
% 0.21/0.49 ~ ( ! [X: $i] :
% 0.21/0.49 ~ ( less @ X @ X )
% 0.21/0.49 & ! [X: $i,Y: $i] :
% 0.21/0.49 ( ~ ( less @ X @ Y )
% 0.21/0.49 | ~ ( less @ Y @ X ) )
% 0.21/0.49 & ! [X: $i] : ( divides @ X @ X )
% 0.21/0.49 & ! [X: $i,Y: $i,Z: $i] :
% 0.21/0.49 ( ~ ( divides @ X @ Y )
% 0.21/0.49 | ~ ( divides @ Y @ Z )
% 0.21/0.49 | ( divides @ X @ Z ) )
% 0.21/0.49 & ! [X: $i,Y: $i] :
% 0.21/0.49 ( ~ ( divides @ X @ Y )
% 0.21/0.49 | ~ ( less @ Y @ X ) )
% 0.21/0.49 & ! [X: $i] : ( less @ X @ ( factorial_plus_one @ X ) )
% 0.21/0.49 & ! [X: $i,Y: $i] :
% 0.21/0.49 ( ~ ( divides @ X @ ( factorial_plus_one @ Y ) )
% 0.21/0.49 | ( less @ Y @ X ) )
% 0.21/0.49 & ! [X: $i] :
% 0.21/0.49 ( ( prime @ X )
% 0.21/0.49 | ( divides @ ( prime_divisor @ X ) @ X ) )
% 0.21/0.49 & ! [X: $i] :
% 0.21/0.49 ( ( prime @ X )
% 0.21/0.49 | ( prime @ ( prime_divisor @ X ) ) )
% 0.21/0.49 & ! [X: $i] :
% 0.21/0.49 ( ( prime @ X )
% 0.21/0.49 | ( less @ ( prime_divisor @ X ) @ X ) )
% 0.21/0.49 & ( prime @ a )
% 0.21/0.49 & ! [X: $i] :
% 0.21/0.49 ( ~ ( prime @ X )
% 0.21/0.49 | ~ ( less @ a @ X )
% 0.21/0.49 | ( less @ ( factorial_plus_one @ a ) @ X ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.5TQuqHAwmA/cvc5---1.0.5_8368.p...
% 0.21/0.49 (declare-sort $$unsorted 0)
% 0.21/0.49 (declare-fun tptp.a () $$unsorted)
% 0.21/0.49 (declare-fun tptp.factorial_plus_one ($$unsorted) $$unsorted)
% 0.21/0.49 (declare-fun tptp.less ($$unsorted $$unsorted) Bool)
% 0.21/0.49 (declare-fun tptp.prime ($$unsorted) Bool)
% 0.21/0.49 (declare-fun tptp.prime_divisor ($$unsorted) $$unsorted)
% 0.21/0.49 (declare-fun tptp.divides ($$unsorted $$unsorted) Bool)
% 0.21/0.49 (assert (not (not (and (forall ((X $$unsorted)) (not (@ (@ tptp.less X) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.less X) Y)) (not (@ (@ tptp.less Y) X)))) (forall ((X $$unsorted)) (@ (@ tptp.divides X) X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.divides X))) (or (not (@ _let_1 Y)) (not (@ (@ tptp.divides Y) Z)) (@ _let_1 Z)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.divides X) Y)) (not (@ (@ tptp.less Y) X)))) (forall ((X $$unsorted)) (@ (@ tptp.less X) (@ tptp.factorial_plus_one X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.divides X) (@ tptp.factorial_plus_one Y))) (@ (@ tptp.less Y) X))) (forall ((X $$unsorted)) (or (@ tptp.prime X) (@ (@ tptp.divides (@ tptp.prime_divisor X)) X))) (forall ((X $$unsorted)) (or (@ tptp.prime X) (@ tptp.prime (@ tptp.prime_divisor X)))) (forall ((X $$unsorted)) (or (@ tptp.prime X) (@ (@ tptp.less (@ tptp.prime_divisor X)) X))) (@ tptp.prime tptp.a) (forall ((X $$unsorted)) (or (not (@ tptp.prime X)) (not (@ (@ tptp.less tptp.a) X)) (@ (@ tptp.less (@ tptp.factorial_plus_one tptp.a)) X)))))))
% 0.21/0.55 (set-info :filename cvc5---1.0.5_8368)
% 0.21/0.55 (check-sat-assuming ( true ))
% 0.21/0.55 ------- get file name : TPTP file name is NUM016^5
% 0.21/0.55 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8368.smt2...
% 0.21/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.55 % SZS status Theorem for NUM016^5
% 0.21/0.55 % SZS output start Proof for NUM016^5
% 0.21/0.55 (
% 0.21/0.55 (let ((_let_1 (and (forall ((X $$unsorted)) (not (@ (@ tptp.less X) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.less X) Y)) (not (@ (@ tptp.less Y) X)))) (forall ((X $$unsorted)) (@ (@ tptp.divides X) X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.divides X))) (or (not (@ _let_1 Y)) (not (@ (@ tptp.divides Y) Z)) (@ _let_1 Z)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.divides X) Y)) (not (@ (@ tptp.less Y) X)))) (forall ((X $$unsorted)) (@ (@ tptp.less X) (@ tptp.factorial_plus_one X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.divides X) (@ tptp.factorial_plus_one Y))) (@ (@ tptp.less Y) X))) (forall ((X $$unsorted)) (or (@ tptp.prime X) (@ (@ tptp.divides (@ tptp.prime_divisor X)) X))) (forall ((X $$unsorted)) (or (@ tptp.prime X) (@ tptp.prime (@ tptp.prime_divisor X)))) (forall ((X $$unsorted)) (or (@ tptp.prime X) (@ (@ tptp.less (@ tptp.prime_divisor X)) X))) (@ tptp.prime tptp.a) (forall ((X $$unsorted)) (or (not (@ tptp.prime X)) (not (@ (@ tptp.less tptp.a) X)) (@ (@ tptp.less (@ tptp.factorial_plus_one tptp.a)) X)))))) (let ((_let_2 (not (not _let_1)))) (let ((_let_3 (forall ((X $$unsorted)) (or (not (ho_6 k_7 X)) (not (ho_6 (ho_5 k_4 tptp.a) X)) (ho_6 (ho_5 k_4 (ho_3 k_2 tptp.a)) X))))) (let ((_let_4 (ho_3 k_2 tptp.a))) (let ((_let_5 (ho_3 k_8 _let_4))) (let ((_let_6 (ho_5 k_4 _let_4))) (let ((_let_7 (ho_6 _let_6 _let_5))) (let ((_let_8 (ho_5 k_4 tptp.a))) (let ((_let_9 (ho_6 _let_8 _let_5))) (let ((_let_10 (not _let_9))) (let ((_let_11 (ho_6 k_7 _let_5))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10 _let_7))) (let ((_let_14 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_15 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_16 (forall ((u |u_(-> $$unsorted $$unsorted)|) (e $$unsorted) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_17 (forall ((x |u_(-> $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_18 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_19 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_20 (ho_6 k_7 tptp.a))) (let ((_let_21 (forall ((X $$unsorted)) (or (ho_6 k_7 X) (ho_6 (ho_5 k_4 (ho_3 k_8 X)) X))))) (let ((_let_22 (forall ((X $$unsorted)) (or (ho_6 k_7 X) (ho_6 k_7 (ho_3 k_8 X)))))) (let ((_let_23 (forall ((X $$unsorted)) (or (ho_6 k_7 X) (ho_6 (ho_5 k_9 (ho_3 k_8 X)) X))))) (let ((_let_24 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (ho_6 (ho_5 k_9 X) (ho_3 k_2 Y))) (ho_6 (ho_5 k_4 Y) X))))) (let ((_let_25 (forall ((X $$unsorted)) (ho_6 (ho_5 k_4 X) (ho_3 k_2 X))))) (let ((_let_26 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (ho_6 (ho_5 k_9 X) Y)) (not (ho_6 (ho_5 k_4 Y) X)))))) (let ((_let_27 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (ho_5 k_9 X))) (or (not (ho_6 _let_1 Y)) (not (ho_6 (ho_5 k_9 Y) Z)) (ho_6 _let_1 Z)))))) (let ((_let_28 (forall ((X $$unsorted)) (ho_6 (ho_5 k_9 X) X)))) (let ((_let_29 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (ho_6 (ho_5 k_4 X) Y)) (not (ho_6 (ho_5 k_4 Y) X)))))) (let ((_let_30 (forall ((X $$unsorted)) (not (ho_6 (ho_5 k_4 X) X))))) (let ((_let_31 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_1 (and _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_3)))))) (PREPROCESS :args ((and _let_19 _let_18 _let_17 _let_16 _let_15 _let_14)))) :args ((and _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_3 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14))))) (let ((_let_32 (AND_ELIM _let_31 :args (11)))) (let ((_let_33 (not _let_13))) (let ((_let_34 (ho_6 k_7 _let_4))) (let ((_let_35 (or _let_34 _let_11))) (let ((_let_36 (_let_22))) (let ((_let_37 (ho_6 _let_6 _let_4))) (let ((_let_38 (ho_6 _let_8 _let_4))) (let ((_let_39 (not _let_38))) (let ((_let_40 (not _let_34))) (let ((_let_41 (or _let_40 _let_39 _let_37))) (let ((_let_42 (_let_3))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 (_let_25))) (let ((_let_45 (_let_30))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_37 _let_39 _let_40 (not _let_41)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 k_4 X)))) :args _let_45)) (AND_ELIM _let_31 :args (0)) :args ((not _let_37) false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (tptp.a QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 k_4 X)))) :args _let_44)) (AND_ELIM _let_31 :args (5)) :args (_let_38 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_6 _let_8 X) false))))) :args _let_42)) _let_32 :args (_let_41 false _let_3)) :args (_let_40 true _let_37 false _let_38 false _let_41)))) (let ((_let_47 (ho_6 (ho_5 k_9 _let_5) _let_4))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_9))) (let ((_let_50 (_let_24))) (let ((_let_51 (or _let_34 _let_47))) (let ((_let_52 (_let_23))) (let ((_let_53 (not _let_7))) (let ((_let_54 (ho_6 (ho_5 k_4 _let_5) _let_4))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53))) (let ((_let_57 (_let_29))) (let ((_let_58 (or _let_34 _let_54))) (let ((_let_59 (_let_21))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_7 _let_10 _let_12 _let_33))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_53 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_34 _let_54 (not _let_58)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_6 k_7 X) true))))) :args _let_59)) (AND_ELIM _let_31 :args (9)) :args (_let_58 false _let_21)) :args (_let_54 true _let_34 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (_let_5 _let_4 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_6 (ho_5 k_4 X) Y) false))))) :args _let_57)) (AND_ELIM _let_31 :args (1)) :args (_let_56 false _let_29)) :args (_let_53 false _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_9 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_34 _let_47 (not _let_51)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_52) :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_6 k_7 X) true))))) :args _let_52)) (AND_ELIM _let_31 :args (7)) :args (_let_51 false _let_23)) :args (_let_47 true _let_34 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (_let_5 tptp.a QUANTIFIERS_INST_E_MATCHING ((not (= (ho_6 (ho_5 k_9 X) (ho_3 k_2 Y)) false))))) :args _let_50)) (AND_ELIM _let_31 :args (6)) :args (_let_49 false _let_24)) :args (_let_9 false _let_47 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_11 (not _let_35)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_36) :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_8 X)))) :args _let_36)) (AND_ELIM _let_31 :args (8)) :args (_let_35 false _let_22)) :args (_let_11 true _let_34 false _let_35)) :args (_let_33 true _let_7 false _let_9 false _let_11)) _let_32 :args (false true _let_13 false _let_3)) :args (_let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55 )
% 0.21/0.55 % SZS output end Proof for NUM016^5
% 0.21/0.55 % cvc5---1.0.5 exiting
% 0.21/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------