TSTP Solution File: NUM635^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM635^2 : 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 10:45:53 EDT 2023
% Result : Theorem 0.23s 0.57s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : NUM635^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Aug 25 12:35:26 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.23/0.53 %----Proving TH0
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 % File : NUM635^2 : TPTP v8.1.2. Released v3.7.0.
% 0.23/0.57 % Domain : Number Theory
% 0.23/0.57 % Problem : Landau theorem 1
% 0.23/0.57 % Version : Especial.
% 0.23/0.57 % English :
% 0.23/0.57
% 0.23/0.57 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.23/0.57 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.23/0.57 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.23/0.57 % Source : [TPTP]
% 0.23/0.57 % Names : satz1 [Lan30]
% 0.23/0.57
% 0.23/0.57 % Status : Theorem
% 0.23/0.57 % Rating : 0.00 v6.0.0, 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
% 0.23/0.57 % Syntax : Number of formulae : 6 ( 1 unt; 2 typ; 0 def)
% 0.23/0.57 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.23/0.57 % Maximal formula atoms : 2 ( 1 avg)
% 0.23/0.57 % Number of connectives : 18 ( 3 ~; 0 |; 1 &; 10 @)
% 0.23/0.57 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.23/0.57 % Maximal formula depth : 8 ( 5 avg)
% 0.23/0.57 % Number of types : 2 ( 0 usr)
% 0.23/0.57 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.23/0.57 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.23/0.57 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.23/0.57 % SPC : TH0_THM_EQU_NAR
% 0.23/0.57
% 0.23/0.57 % Comments :
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 thf(one_type,type,
% 0.23/0.57 one: $i ).
% 0.23/0.57
% 0.23/0.57 thf(succ_type,type,
% 0.23/0.57 succ: $i > $i ).
% 0.23/0.57
% 0.23/0.57 thf(one_is_first,axiom,
% 0.23/0.57 ! [X: $i] :
% 0.23/0.57 ( ( succ @ X )
% 0.23/0.57 != one ) ).
% 0.23/0.57
% 0.23/0.57 thf(succ_injective,axiom,
% 0.23/0.57 ! [X: $i,Y: $i] :
% 0.23/0.57 ( ( ( succ @ X )
% 0.23/0.57 = ( succ @ Y ) )
% 0.23/0.57 => ( X = Y ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(induction,axiom,
% 0.23/0.57 ! [M: $i > $o] :
% 0.23/0.57 ( ( ( M @ one )
% 0.23/0.57 & ! [X: $i] :
% 0.23/0.57 ( ( M @ X )
% 0.23/0.57 => ( M @ ( succ @ X ) ) ) )
% 0.23/0.57 => ! [Y: $i] : ( M @ Y ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(satz1,conjecture,
% 0.23/0.57 ! [X: $i,Y: $i] :
% 0.23/0.57 ( ( X != Y )
% 0.23/0.57 => ( ( succ @ X )
% 0.23/0.57 != ( succ @ Y ) ) ) ).
% 0.23/0.57
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZRep1waEh1/cvc5---1.0.5_3947.p...
% 0.23/0.57 (declare-sort $$unsorted 0)
% 0.23/0.57 (declare-fun tptp.one () $$unsorted)
% 0.23/0.57 (declare-fun tptp.succ ($$unsorted) $$unsorted)
% 0.23/0.57 (assert (forall ((X $$unsorted)) (not (= (@ tptp.succ X) tptp.one))))
% 0.23/0.57 (assert (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ tptp.succ X) (@ tptp.succ Y)) (= X Y))))
% 0.23/0.57 (assert (forall ((M (-> $$unsorted Bool))) (=> (and (@ M tptp.one) (forall ((X $$unsorted)) (=> (@ M X) (@ M (@ tptp.succ X))))) (forall ((Y $$unsorted)) (@ M Y)))))
% 0.23/0.57 (assert (not (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= X Y)) (not (= (@ tptp.succ X) (@ tptp.succ Y)))))))
% 0.23/0.57 (set-info :filename cvc5---1.0.5_3947)
% 0.23/0.57 (check-sat-assuming ( true ))
% 0.23/0.57 ------- get file name : TPTP file name is NUM635^2
% 0.23/0.57 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3947.smt2...
% 0.23/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.57 % SZS status Theorem for NUM635^2
% 0.23/0.57 % SZS output start Proof for NUM635^2
% 0.23/0.57 (
% 0.23/0.57 (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= X Y)) (not (= (@ tptp.succ X) (@ tptp.succ Y)))))))) (let ((_let_2 (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ tptp.succ X) (@ tptp.succ Y)) (= X Y))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (or (= X Y) (not (= (ho_3 k_2 Y) (ho_3 k_2 X))))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (ho_3 k_2 Y) (ho_3 k_2 X))) (= X Y))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X $$unsorted) (Y $$unsorted)) (or (= X Y) (not (= (@ tptp.succ X) (@ tptp.succ Y)))))) (not _let_3)))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_4 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (ho_3 k_2 Y) (ho_3 k_2 X))) (= X Y))) _let_3) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) :args ((or _let_3 (not _let_4)))) (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (@ tptp.succ X) (@ tptp.succ Y))) (= X Y))) _let_4))))) :args (_let_3 false _let_4)) :args (false false _let_3)) :args ((forall ((X $$unsorted)) (not (= (@ tptp.succ X) tptp.one))) _let_2 (forall ((M (-> $$unsorted Bool))) (=> (and (@ M tptp.one) (forall ((X $$unsorted)) (=> (@ M X) (@ M (@ tptp.succ X))))) (forall ((Y $$unsorted)) (@ M Y)))) _let_1 true)))))))
% 0.23/0.57 )
% 0.23/0.57 % SZS output end Proof for NUM635^2
% 0.23/0.57 % cvc5---1.0.5 exiting
% 0.23/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------